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| caption = do Carmo in 1979
| caption = do Carmo in 1979
| birth_date = {{birth date|1928|8|15|df=y}}
| birth_date = {{birth date|1928|8|15|df=y}}
| birth_place = [[Maceió]]
| birth_place = [[Maceió]], [[Alagoas]]
| death_date = {{death date and age|2018|4|30|1928|8|15|df=y}}
| death_date = {{death date and age|2018|4|30|1928|8|15|df=y}}
| death_place = [[Rio de Janeiro]]
| death_place = [[Rio de Janeiro]]
| citizenship =
| citizenship =
| nationality = Brazilian
| nationality = Brazilian
| ethnicity =
| fields = [[Mathematics]]
| fields = [[Mathematics]]
| workplaces = [[Instituto Nacional de Matemática Pura e Aplicada]]
| workplaces = [[Instituto Nacional de Matemática Pura e Aplicada]]
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| influences =
| influences =
| influenced = [[Fernando Codá Marques]]
| influenced = [[Fernando Codá Marques]]
| awards = [[National Order of Scientific Merit (Brazil)|Brazil's National Order of Scientific Merit]] (1995)<br/>[[TWAS Prize]] (1987)<br/>[[American Mathematical Society|AMS Fellow]] (2012)
| awards = [[Guggenheim Fellowship]] (1965, 1968)<br/>
[[National Order of Scientific Merit (Brazil)|Brazil's National Order of Scientific Merit]] (1995)<br/>[[TWAS Prize]] (1987)<br/>[[American Mathematical Society|AMS Fellow]] (2012)
| religion =
| signature = <!--(filename only)-->
| signature = <!--(filename only)-->
| signature_alt =
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}}
}}


'''Manfredo Perdigão do Carmo''' (15 August 1928 – 30 April 2018) was a [[Brazil|Brazilian]] [[mathematician]], specialising in [[differential geometry]]. He spent most of his career at [[Instituto Nacional de Matemática Pura e Aplicada|IMPA]] and was a former president of the [[Brazilian Mathematical Society]].
'''Manfredo Perdigão do Carmo''' (15 August 1928, [[Maceió]] – 30 April 2018, [[Rio de Janeiro]]) was a [[Brazil|Brazilian]] [[mathematician]]. He spent most of his career at [[Instituto Nacional de Matemática Pura e Aplicada|IMPA]] and he is seen as the doyen of [[differential geometry]] in Brazil.<ref>{{Cite journal|last=Gorodski|first=Claudio|last2=Piccione|first2=Paolo|date=2021-06-01|title=Opening note: An homage to Manfredo P. do Carmo|url=https://doi.org/10.1007/s40863-020-00194-0|journal=São Paulo Journal of Mathematical Sciences|language=en|volume=15|issue=1|pages=1–2|doi=10.1007/s40863-020-00194-0|issn=2316-9028}}</ref>

He spent most of his career at [[Instituto Nacional de Matemática Pura e Aplicada|IMPA]], was a former president of the [[Brazilian Mathematical Society]], and is seen as the doyen of


== Education and career ==
== Education and career ==
Do Carmo studied [[civil engineering]] at the [[University of Recife]] from 1947 to 1951. After working a few years as engineer, he accepted a teaching position at the newly created Institute of Physics and Mathematics at Recife.<ref name=":0">{{Cite journal|last=Queiroz|first=Antonio José Melo de|date=2020|title=O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil|url=https://revistas.uece.br/index.php/BOCEHM/article/view/2819|journal=Boletim Cearense de Educação e História da Matemática|language=pt|volume=7|issue=20|pages=266–276|doi=10.30938/bocehm.v7i20.2819|issn=2447-8504}}</ref>
Do Carmo studied [[civil engineering]] at the [[University of Recife]] from 1947 to 1951. After working a few years as engineer, he accepted a teaching position at the newly created Institute of Physics and Mathematics at Recife.<ref name=":0">{{Cite journal|last=Queiroz|first=Antonio José Melo de|date=2020|title=O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil|url=https://revistas.uece.br/index.php/BOCEHM/article/view/2819|journal=Boletim Cearense de Educação e História da Matemática|language=pt|volume=7|issue=20|pages=266–276|doi=10.30938/bocehm.v7i20.2819|issn=2447-8504}}</ref>


On suggestion of [[Elon Lages Lima|Elon Lima]], in 1959 he went to [[Instituto Nacional de Matemática Pura e Aplicada]] to improve his background<ref name=":0">{{Cite journal|last=Queiroz|first=Antonio José Melo de|date=2020|title=O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil|url=https://revistas.uece.br/index.php/BOCEHM/article/view/2819|journal=Boletim Cearense de Educação e História da Matemática|language=pt|volume=7|issue=20|pages=266–276|doi=10.30938/bocehm.v7i20.2819|issn=2447-8504}}</ref><ref name=":1">{{Citation|last=Carmo|first=Manfredo P. do|title=A Summary of the Scientific Activities|date=2012|url=https://doi.org/10.1007/978-3-642-25588-5_1|work=Manfredo P. do Carmo – Selected Papers|pages=1–5|editor-last=do Carmo|editor-first=Manfredo P.|place=Berlin, Heidelberg|publisher=Springer|language=en|doi=10.1007/978-3-642-25588-5_1|isbn=978-3-642-25588-5|access-date=2022-01-31|editor2-last=Tenenblat|editor2-first=Keti}}</ref> and in 1960 he moved to the USA to pursue a Ph.D. in mathematics at the [[University of California, Berkeley]] under the supervision of [[Shiing-Shen Chern]]. He defended his thesis, entitled "''The Cohomology Ring of Certain Kahlerian Manifolds''" in 1963.<ref name="MGP">{{mathgenealogy|id=31508}}</ref>
On suggestion of [[Elon Lages Lima|Elon Lima]], in 1959 he went to [[Instituto Nacional de Matemática Pura e Aplicada]] to improve his background<ref name=":0">{{Cite journal|last=Queiroz|first=Antonio José Melo de|date=2020|title=O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil|url=https://revistas.uece.br/index.php/BOCEHM/article/view/2819|journal=Boletim Cearense de Educação e História da Matemática|language=pt|volume=7|issue=20|pages=266–276|doi=10.30938/bocehm.v7i20.2819|issn=2447-8504}}</ref><ref name=":1">{{Citation|last=Carmo|first=Manfredo P. do|title=A Summary of the Scientific Activities|date=2012|url=https://doi.org/10.1007/978-3-642-25588-5_1|work=Manfredo P. do Carmo – Selected Papers|pages=1–5|editor-last=do Carmo|editor-first=Manfredo P.|place=Berlin, Heidelberg|publisher=Springer|language=en|doi=10.1007/978-3-642-25588-5_1|isbn=978-3-642-25588-5|access-date=2022-01-31|editor2-last=Tenenblat|editor2-first=Keti}}</ref> and in 1960 he moved to the USA to pursue a Ph.D. in mathematics at the [[University of California, Berkeley]] under the supervision of [[Shiing-Shen Chern]]. He defended his thesis, entitled "''The Cohomology Ring of Certain Kahlerian Manifolds''", in 1963.<ref name="MGP">{{mathgenealogy|id=31508}}</ref>


After working again at [[University of Recife]] and at the [[University of Brasília|University of Brasilia]], in 1966 he become professor at [[Instituto Nacional de Matemática Pura e Aplicada]] (IMPA) in [[Rio de Janeiro]]. From 2003 to his death he was [[Emeritus|emeritus professor]].<ref name=":0">{{Cite journal|last=Queiroz|first=Antonio José Melo de|date=2020|title=O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil|url=https://revistas.uece.br/index.php/BOCEHM/article/view/2819|journal=Boletim Cearense de Educação e História da Matemática|language=pt|volume=7|issue=20|pages=266–276|doi=10.30938/bocehm.v7i20.2819|issn=2447-8504}}</ref>
After working again at [[University of Recife]] and at the [[University of Brasília|University of Brasilia]], in 1966 he became professor at [[Instituto Nacional de Matemática Pura e Aplicada]] (IMPA) in [[Rio de Janeiro]]. From 2003 to his death he was [[Emeritus|emeritus professor]].<ref name=":0">{{Cite journal|last=Queiroz|first=Antonio José Melo de|date=2020|title=O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil|url=https://revistas.uece.br/index.php/BOCEHM/article/view/2819|journal=Boletim Cearense de Educação e História da Matemática|language=pt|volume=7|issue=20|pages=266–276|doi=10.30938/bocehm.v7i20.2819|issn=2447-8504}}</ref>


Do Carmo was a [[Guggenheim Fellowships|Guggenheim Fellow]] in [[List of Guggenheim Fellowships awarded in 1965|1965]] and [[List of Guggenheim Fellowships awarded in 1968|1968]].<ref name="gug">[https://web.archive.org/web/20150113232909/http://www.gf.org/fellows/2288-manfredo-perdigao-do-carmo Biography from the Guggenheim Foundation]</ref><ref>{{Cite web|title=John Simon Guggenheim Foundation {{!}} Manfredo Perdigao do Carmo|url=https://www.gf.org/fellows/all-fellows/manfredo-perdigao-do-carmo/|access-date=2022-01-31|language=en-US}}</ref> In 1978 he was [[List of International Congresses of Mathematicians Plenary and Invited Speakers#1978, Helsinki|invited speaker]] at the [[International Congress of Mathematicians]] held in [[Helsinki]] (the theme was "''Minimal Surfaces: Stability and Finiteness''").<ref>{{Cite book|url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1978.1/ICM1978.1.ocr.pdf|title=Proceedings of the International Congress of Mathematician 1978|year=1980|editor-last=Lehto|editor-first=Olii|editor-link=Olli Lehto|location=Helsinki|pages=401}}</ref><ref>{{citation|last=do Carmo|first=Manfredo P.|title=Proceedings of the International Congress of Mathematicians (Helsinki, 1978)|pages=401–405|year=1980|contribution=Minimal surfaces: stability and finiteness|publisher=Acad. Sci. Fennica, Helsinki|mr=562633}}.</ref>
Do Carmo was a [[Guggenheim Fellowships|Guggenheim Fellow]] in [[List of Guggenheim Fellowships awarded in 1965|1965]] and [[List of Guggenheim Fellowships awarded in 1968|1968]].<ref name="gug">[https://web.archive.org/web/20150113232909/http://www.gf.org/fellows/2288-manfredo-perdigao-do-carmo Biography from the Guggenheim Foundation]</ref><ref>{{Cite web|title=John Simon Guggenheim Foundation {{!}} Manfredo Perdigao do Carmo|url=https://www.gf.org/fellows/all-fellows/manfredo-perdigao-do-carmo/|access-date=2022-01-31|language=en-US}}</ref> In 1978 he was [[List of International Congresses of Mathematicians Plenary and Invited Speakers#1978, Helsinki|invited speaker]] at the [[International Congress of Mathematicians]] held in [[Helsinki]].<ref>{{Cite book|url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1978.1/ICM1978.1.ocr.pdf|title=Proceedings of the International Congress of Mathematician 1978|year=1980|editor-last=Lehto|editor-first=Olii|editor-link=Olli Lehto|location=Helsinki|pages=401}}</ref><ref>{{citation|last=do Carmo|first=Manfredo P.|title=Proceedings of the International Congress of Mathematicians (Helsinki, 1978)|pages=401–405|year=1980|contribution=Minimal surfaces: stability and finiteness|publisher=Acad. Sci. Fennica, Helsinki|mr=562633}}.</ref><ref>{{Citation|last=Carmo|first=Manfredo P. do|title=Minimal Surfaces: Stability and Finiteness|date=2012|url=https://doi.org/10.1007/978-3-642-25588-5_12|work=Manfredo P. do Carmo – Selected Papers|pages=139–143|editor-last=do Carmo|editor-first=Manfredo P.|place=Berlin, Heidelberg|publisher=Springer|language=en|doi=10.1007/978-3-642-25588-5_12|isbn=978-3-642-25588-5|access-date=2022-02-01|editor2-last=Tenenblat|editor2-first=Keti}}</ref>


He served as president of the [[Brazilian Mathematical Society]] in the term 1971-1973.<ref>{{Cite web|title=Diretorias Anteriores – SBM – Sociedade Brasileira de Matemática|url=https://sbm.org.br/diretorias-anteriores/|access-date=2022-01-31|language=pt-BR}}</ref> He was elected a member of the [[Brazilian Academy of Sciences]] in 1970<ref>{{Cite web|title=Manfredo Perdigão do Carmo – ABC|url=https://www.abc.org.br/membro/manfredo-perdigao-do-carmo/|access-date=2022-01-31|language=pt-BR}}</ref>, a member of the [[The World Academy of Sciences]] (TWAS) in 1997<ref name=":2">{{Cite web|title=do Carmo, Manfredo P.|url=https://twas.org/directory/do-carmo-manfredo-p|access-date=2022-01-31|website=TWAS|language=en}}</ref> and a fellow of the [[American Mathematical Society]] In 2013.<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2015-01-13.</ref>
He served as president of the [[Brazilian Mathematical Society]] in the term 1971-1973.<ref>{{Cite web|title=Diretorias Anteriores – SBM – Sociedade Brasileira de Matemática|url=https://sbm.org.br/diretorias-anteriores/|access-date=2022-01-31|language=pt-BR}}</ref> He was elected a member of the [[Brazilian Academy of Sciences]] in 1970<ref>{{Cite web|title=Manfredo Perdigão do Carmo – ABC|url=https://www.abc.org.br/membro/manfredo-perdigao-do-carmo/|access-date=2022-01-31|language=pt-BR}}</ref>, a member of the [[The World Academy of Sciences]] (TWAS) in 1997<ref name=":2">{{Cite web|title=do Carmo, Manfredo P.|url=https://twas.org/directory/do-carmo-manfredo-p|access-date=2022-01-31|website=TWAS|language=en}}</ref> and a fellow of the [[American Mathematical Society]] In 2013.<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2015-01-13.</ref>
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== Research ==
== Research ==
Do Carmo's research involved [[Riemannian manifold|Riemannian geometry]] and the [[differential geometry of surfaces]].<ref name=":1" /> In particular, he worked on [[Rigidity (mathematics)|rigidity]] and convexity of [[Isometric immersion|isometric immersions]],<ref>{{Cite journal|last=do Carmo|first=M. P.|last2=Warner|first2=F. W.|date=1970-01-01|title=Rigidity and convexity of hypersurfaces in spheres|url=https://projecteuclid.org/journals/journal-of-differential-geometry/volume-4/issue-2/Rigidity-and-convexity-of-hypersurfaces-in-spheres/10.4310/jdg/1214429378.full|journal=Journal of Differential Geometry|volume=4|issue=2|doi=10.4310/jdg/1214429378|issn=0022-040X}}</ref><ref>{{Cite journal|last=doCarmo|first=Manfredo P.|last2=Lima|first2=Elon|date=1969-05-01|title=Isometric immersions with semi-definite second quadratic forms|url=https://doi.org/10.1007/BF01899010|journal=Archiv der Mathematik|language=en|volume=20|issue=2|pages=173–175|doi=10.1007/BF01899010|issn=1420-8938}}</ref> stability of [[hypersurface]]s<ref>{{Cite journal|last=Barbosa|first=João Lucas|last2=do Carmo|first2=Manfredo|date=1984-09-01|title=Stability of hypersurfaces with constant mean curvature|url=https://doi.org/10.1007/BF01215045|journal=Mathematische Zeitschrift|language=en|volume=185|issue=3|pages=339–353|doi=10.1007/BF01215045|issn=1432-1823}}</ref><ref>{{Cite journal|last=Barbosa|first=J. Lucas|last2=do Carmo|first2=Manfredo|last3=Eschenburg|first3=Jost|date=1988-03-01|title=Stability of hypersurfaces of constant mean curvature in Riemannian manifolds|url=https://doi.org/10.1007/BF01161634|journal=Mathematische Zeitschrift|language=en|volume=197|issue=1|pages=123–138|doi=10.1007/BF01161634|issn=1432-1823}}</ref> and of [[minimal surface]]s,<ref>{{Cite journal|last=Barbosa|first=J. L.|last2=Carmo|first2=M. Do|date=1976|title=On the Size of a Stable Minimal Surface in R3|url=https://www.jstor.org/stable/2373899|journal=American Journal of Mathematics|volume=98|issue=2|pages=515–528|doi=10.2307/2373899|issn=0002-9327}}</ref><ref>{{Cite journal|last=do Carmo|first=M.|last2=Peng|first2=C. K.|date=1979|title=Stable complete minimal surfaces in 𝑅³ are planes|url=https://www.ams.org/bull/1979-01-06/S0273-0979-1979-14689-5/|journal=Bulletin of the American Mathematical Society|language=en|volume=1|issue=6|pages=903–906|doi=10.1090/S0273-0979-1979-14689-5|issn=0273-0979}}</ref> [[topology]] of [[manifold]]s,<ref>{{Cite journal|last=do Carmo|first=Manfredo|last2=Xia|first2=Changyu|date=2000-02-01|title=Ricci curvature and the topology of open manifolds|url=https://doi.org/10.1007/s002080050018|journal=Mathematische Annalen|language=en|volume=316|issue=2|pages=391–400|doi=10.1007/s002080050018|issn=1432-1807}}</ref> [[isoperimetric problem]]s,<ref>{{Cite journal|last=Barbosa|first=João Lucas|last2=Carmo|first2=Manfredo do|date=1978-10-01|title=A proof of a general isoperimetric inequality for surfaces|url=https://doi.org/10.1007/BF01186367|journal=Mathematische Zeitschrift|language=en|volume=162|issue=3|pages=245–261|doi=10.1007/BF01186367|issn=1432-1823}}</ref> [[Minimal submanifold|minimal submanifolds]] of a [[sphere]],<ref>{{Citation|last=Chern|first=S. S.|title=Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length|date=1970|url=https://doi.org/10.1007/978-3-642-48272-4_2|work=Functional Analysis and Related Fields: Proceedings of a Conference in honor of Professor Marshall Stone, held at the University of Chicago, May 1968|pages=59–75|editor-last=Browder|editor-first=Felix E.|place=Berlin, Heidelberg|publisher=Springer|language=en|doi=10.1007/978-3-642-48272-4_2|isbn=978-3-642-48272-4|access-date=2022-02-01|last2=do Carmo|first2=M.|last3=Kobayashi|first3=S.}}</ref><ref>{{Cite journal|last=Carmo|first=Manfredo P. Do|last2=Wallach|first2=Nolan R.|date=1971|title=Minimal Immersions of Spheres into Spheres|url=https://www.jstor.org/stable/1970752|journal=Annals of Mathematics|volume=93|issue=1|pages=43–62|doi=10.2307/1970752|issn=0003-486X}}</ref> and manifolds of constant [[mean curvature]]<ref>{{Cite journal|last=do Carmo|first=Manfredo P.|last2=Dajczer|first2=Marcos|date=1982-01-01|title=Helicoidal surfaces with constant mean curvature|url=https://projecteuclid.org/journals/tohoku-mathematical-journal/volume-34/issue-3/Helicoidal-surfaces-with-constant-mean-curvature/10.2748/tmj/1178229204.full|journal=Tohoku Mathematical Journal|volume=34|issue=3|doi=10.2748/tmj/1178229204|issn=0040-8735}}</ref><ref>{{Cite journal|last=Carmo|first=M. Do|last2=Dajczer|first2=M.|date=1983|title=Rotation Hypersurfaces in Spaces of Constant Curvature|url=https://www.jstor.org/stable/1999231|journal=Transactions of the American Mathematical Society|volume=277|issue=2|pages=685–709|doi=10.2307/1999231|issn=0002-9947}}</ref><ref>{{Cite journal|last=Alencar|first=Hilário|last2=do Carmo|first2=Manfredo|date=1994|title=Hypersurfaces with constant mean curvature in spheres|url=https://www.ams.org/proc/1994-120-04/S0002-9939-1994-1172943-2/|journal=Proceedings of the American Mathematical Society|language=en|volume=120|issue=4|pages=1223–1229|doi=10.1090/S0002-9939-1994-1172943-2|issn=0002-9939}}</ref><ref>{{Cite journal|last=Bérard|first=P.|last2=do Carmo|first2=M.|last3=Santos|first3=W.|date=1998-06-01|title=Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature|url=https://doi.org/10.1023/A:1006542723958|journal=Annals of Global Analysis and Geometry|language=en|volume=16|issue=3|pages=273–290|doi=10.1023/A:1006542723958|issn=1572-9060}}</ref> and vanishing [[scalar curvature]].<ref>{{Cite journal|last=Barbosa|first=J. L. M.|last2=Carmo|first2=M. P. Do|date=2005-09-01|title=On Stability of Cones in Rn+1 with Zero Scalar Curvature|url=https://doi.org/10.1007/s10455-005-0039-5|journal=Annals of Global Analysis and Geometry|language=en|volume=28|issue=2|pages=107–122|doi=10.1007/s10455-005-0039-5|issn=1572-9060}}</ref>
Do Carmo's research involved [[Riemannian manifold]]s, [[topology]] of [[manifold]]s, rigidity and convexity of [[Isometric immersion|isometric immersions]], [[minimal surface]]s, stability of [[hypersurface]]s, [[isoperimetric problem]]s, [[Minimal submanifold|minimal submanifolds]] of a [[sphere]], and manifolds of constant [[mean curvature]] and vanishing [[scalar curvature]].<ref name="gug" /><ref name=":1">{{Citation|last=Carmo|first=Manfredo P. do|title=A Summary of the Scientific Activities|date=2012|url=https://doi.org/10.1007/978-3-642-25588-5_1|work=Manfredo P. do Carmo – Selected Papers|pages=1–5|editor-last=do Carmo|editor-first=Manfredo P.|place=Berlin, Heidelberg|publisher=Springer|language=en|doi=10.1007/978-3-642-25588-5_1|isbn=978-3-642-25588-5|access-date=2022-01-31|editor2-last=Tenenblat|editor2-first=Keti}}</ref>


Do Carmo is also known for his textbooks. They were translated into many languages and used in courses from universities such as [[Harvard University|Harvard]] and [[Columbia University|Columbia]].<ref>{{cite book|editor=Shozo Motoyama|title=Prelúdio para uma história: ciência e tecnologia no Brasil|url=https://books.google.com/books?id=z_BNPYRNmyYC&pg=PA358|year=2004|publisher=EdUSP|language=Portuguese|isbn=978-85-314-0797-0|page=358}}</ref><ref name=":0">{{Cite journal|last=Queiroz|first=Antonio José Melo de|date=2020|title=O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil|url=https://revistas.uece.br/index.php/BOCEHM/article/view/2819|journal=Boletim Cearense de Educação e História da Matemática|language=pt|volume=7|issue=20|pages=266–276|doi=10.30938/bocehm.v7i20.2819|issn=2447-8504}}</ref>
Do Carmo published more than 100 papers in peer-reviewed journals;<ref>{{Cite web|title=zbMATH Open - the first resource for mathematics|url=https://zbmath.org/authors/?q=ai:do-carmo.manfredo-perdigao|access-date=2022-02-01|website=zbmath.org}}</ref> in 2012 a selection of his works was published by [[Springer Science+Business Media|Springer]].<ref>{{Cite journal|last=do Carmo|first=Manfredo P.|date=2012|title=Manfredo P. do Carmo – Selected Papers|url=https://doi.org/10.1007/978-3-642-25588-5|language=en-gb|doi=10.1007/978-3-642-25588-5}}</ref> He is also known for his textbooks: they were translated into many languages and used in courses from universities such as [[Harvard University|Harvard]] and [[Columbia University|Columbia]].<ref>{{cite book|url=https://books.google.com/books?id=z_BNPYRNmyYC&pg=PA358|title=Prelúdio para uma história: ciência e tecnologia no Brasil|publisher=EdUSP|year=2004|isbn=978-85-314-0797-0|editor=Shozo Motoyama|page=358|language=Portuguese}}</ref><ref name=":0" />


He supervised 27 PhD students, including [[Celso Costa]], [[Marcos Dajczer]] and [[Keti Tenenblat]].<ref name="MGP" />
He supervised 27 PhD students, including [[Celso Costa]], [[Marcos Dajczer]] and [[Keti Tenenblat]].<ref name="MGP" />
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* ''Member'', [[Brazilian Academy of Sciences]] (1971)
* ''Member'', [[Brazilian Academy of Sciences]] (1971)
* ''Invited Lecturer'', [[International Congress of Mathematicians|ICM]] (1978)
* ''Invited Lecturer'', [[International Congress of Mathematicians|ICM]] (1978)
* ''Almirante Álvaro Alberto Award'', [[CNPq]] (1984)
* ''Almirante Álvaro Alberto Award'', [[CNPq]] (1984)<ref>{{Cite web|title=:: CNPq - Prêmio Almirante Álvaro Alberto ::|url=http://www.premioalvaroalberto.cnpq.br/laureados.html|access-date=2022-02-01|website=www.premioalvaroalberto.cnpq.br}}</ref>
* ''[[Honorary degree]]'', [[Federal University of Alagoas]] (1991)
* ''[[Honorary degree]]'', [[Federal University of Alagoas]] (1991)
* [[TWAS Prize#Mathematics|Third World Academy of Sciences Prize]] (1992)
* [[TWAS Prize#Mathematics|Third World Academy of Sciences Prize]] (1992)
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* ''Honorary Member'', [[Brazilian Mathematical Society]] (2009)
* ''Honorary Member'', [[Brazilian Mathematical Society]] (2009)
* ''[[Honorary degree]]'', [[Federal University of Amazonas]] (2012)
* ''[[Honorary degree]]'', [[Federal University of Amazonas]] (2012)
* ''[[Honorary degree]]'', [[University of Murcia]] (2012)<ref>{{Cite web|title=Professor Manfredo P. Do Carmo will be awarded the honorary degree Doctor Honoris Causa by the Universidad de Murcia {{!}} European Mathematical Society|url=https://euro-math-soc.eu/news/12/02/28/professor-manfredo-p-do-carmo-will-be-awarded-honorary-degree-doctor-honoris-causa|access-date=2022-02-01|website=euro-math-soc.eu}}</ref>
* ''[[Honorary degree]]'', [[University of Murcia]] (2012)
* ''Fellow'', [[American Mathematical Society]] (2012)
* ''Fellow'', [[American Mathematical Society]] (2012)


Line 75: Line 76:
*''Riemannian Geometry'', Birkhäuser, 1992
*''Riemannian Geometry'', Birkhäuser, 1992
*''Differential Forms and Applications'', Springer Verlag, Universitext, 1994
*''Differential Forms and Applications'', Springer Verlag, Universitext, 1994
*''Manfredo P. do Carmo – Selected Papers'' (ed. Keti Tenenblat), Springer, 2012, first volume of the collection “Selected Works of Outstanding Brazilian Mathematicians”
*''Manfredo P. do Carmo – Selected Papers'' (ed. Keti Tenenblat), Springer, 2012, first volume of the collection “Selected Works of Outstanding Brazilian Mathematicians” {{ISBN|978-3-642-25587-8}}
*Eduardo Wagner, Augusto Cezar de Oliveira Morgado, Manfredo Perdigão do Carmo . ''Trigonometria – Números Complexos'' {{ISBN|8583370168}}
*Eduardo Wagner, Augusto Cezar de Oliveira Morgado, Manfredo Perdigão do Carmo . ''Trigonometria – Números Complexos'' {{ISBN|8583370168}}


Revision as of 23:32, 1 February 2022

Manfredo do Carmo
do Carmo in 1979
Born(1928-08-15)15 August 1928
Maceió, Alagoas
Died30 April 2018(2018-04-30) (aged 89)
Rio de Janeiro
NationalityBrazilian
Alma materUniversity of California, Berkeley
AwardsGuggenheim Fellowship (1965, 1968)
Brazil's National Order of Scientific Merit (1995)
TWAS Prize (1987)
AMS Fellow (2012)
Scientific career
FieldsMathematics
InstitutionsInstituto Nacional de Matemática Pura e Aplicada
Thesis The Cohomology Ring of Certain Kahlerian Manifolds  (1963)
Doctoral advisorShiing-Shen Chern
Doctoral studentsCelso Costa
Marcos Dajczer
Keti Tenenblat

Manfredo Perdigão do Carmo (15 August 1928, Maceió – 30 April 2018, Rio de Janeiro) was a Brazilian mathematician. He spent most of his career at IMPA and he is seen as the doyen of differential geometry in Brazil.[1]

He spent most of his career at IMPA, was a former president of the Brazilian Mathematical Society, and is seen as the doyen of

Education and career

Do Carmo studied civil engineering at the University of Recife from 1947 to 1951. After working a few years as engineer, he accepted a teaching position at the newly created Institute of Physics and Mathematics at Recife.[2]

On suggestion of Elon Lima, in 1959 he went to Instituto Nacional de Matemática Pura e Aplicada to improve his background[2][3] and in 1960 he moved to the USA to pursue a Ph.D. in mathematics at the University of California, Berkeley under the supervision of Shiing-Shen Chern. He defended his thesis, entitled "The Cohomology Ring of Certain Kahlerian Manifolds", in 1963.[4]

After working again at University of Recife and at the University of Brasilia, in 1966 he became professor at Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. From 2003 to his death he was emeritus professor.[2]

Do Carmo was a Guggenheim Fellow in 1965 and 1968.[5][6] In 1978 he was invited speaker at the International Congress of Mathematicians held in Helsinki.[7][8][9]

He served as president of the Brazilian Mathematical Society in the term 1971-1973.[10] He was elected a member of the Brazilian Academy of Sciences in 1970[11], a member of the The World Academy of Sciences (TWAS) in 1997[12] and a fellow of the American Mathematical Society In 2013.[13]

He received the Brazilian National Prize for Science and Technology of the National Council for Scientific and Technological Development in 1984, the TWAS Prize in Mathematics in 1992[12][14] and the National Order of Scientific Merit in 1995.

Do Carmo died on 30 April 2018 at the age of 89.[15][16][17]

Research

Do Carmo's research involved Riemannian geometry and the differential geometry of surfaces.[3] In particular, he worked on rigidity and convexity of isometric immersions,[18][19] stability of hypersurfaces[20][21] and of minimal surfaces,[22][23] topology of manifolds,[24] isoperimetric problems,[25] minimal submanifolds of a sphere,[26][27] and manifolds of constant mean curvature[28][29][30][31] and vanishing scalar curvature.[32]

Do Carmo published more than 100 papers in peer-reviewed journals;[33] in 2012 a selection of his works was published by Springer.[34] He is also known for his textbooks: they were translated into many languages and used in courses from universities such as Harvard and Columbia.[35][2]

He supervised 27 PhD students, including Celso Costa, Marcos Dajczer and Keti Tenenblat.[4]

Awards and honors

Books

  • Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976
  • Riemannian Geometry, Birkhäuser, 1992
  • Differential Forms and Applications, Springer Verlag, Universitext, 1994
  • Manfredo P. do Carmo – Selected Papers (ed. Keti Tenenblat), Springer, 2012, first volume of the collection “Selected Works of Outstanding Brazilian Mathematicians” ISBN 978-3-642-25587-8
  • Eduardo Wagner, Augusto Cezar de Oliveira Morgado, Manfredo Perdigão do Carmo . Trigonometria – Números Complexos ISBN 8583370168

References

  1. ^ Gorodski, Claudio; Piccione, Paolo (2021-06-01). "Opening note: An homage to Manfredo P. do Carmo". São Paulo Journal of Mathematical Sciences. 15 (1): 1–2. doi:10.1007/s40863-020-00194-0. ISSN 2316-9028.
  2. ^ a b c d Queiroz, Antonio José Melo de (2020). "O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil". Boletim Cearense de Educação e História da Matemática (in Portuguese). 7 (20): 266–276. doi:10.30938/bocehm.v7i20.2819. ISSN 2447-8504.
  3. ^ a b Carmo, Manfredo P. do (2012), do Carmo, Manfredo P.; Tenenblat, Keti (eds.), "A Summary of the Scientific Activities", Manfredo P. do Carmo – Selected Papers, Berlin, Heidelberg: Springer, pp. 1–5, doi:10.1007/978-3-642-25588-5_1, ISBN 978-3-642-25588-5, retrieved 2022-01-31
  4. ^ a b Manfredo do Carmo at the Mathematics Genealogy Project
  5. ^ Biography from the Guggenheim Foundation
  6. ^ "John Simon Guggenheim Foundation | Manfredo Perdigao do Carmo". Retrieved 2022-01-31.
  7. ^ Lehto, Olii, ed. (1980). Proceedings of the International Congress of Mathematician 1978 (PDF). Helsinki. p. 401.{{cite book}}: CS1 maint: location missing publisher (link)
  8. ^ do Carmo, Manfredo P. (1980), "Minimal surfaces: stability and finiteness", Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, pp. 401–405, MR 0562633.
  9. ^ Carmo, Manfredo P. do (2012), do Carmo, Manfredo P.; Tenenblat, Keti (eds.), "Minimal Surfaces: Stability and Finiteness", Manfredo P. do Carmo – Selected Papers, Berlin, Heidelberg: Springer, pp. 139–143, doi:10.1007/978-3-642-25588-5_12, ISBN 978-3-642-25588-5, retrieved 2022-02-01
  10. ^ "Diretorias Anteriores – SBM – Sociedade Brasileira de Matemática" (in Brazilian Portuguese). Retrieved 2022-01-31.
  11. ^ "Manfredo Perdigão do Carmo – ABC" (in Brazilian Portuguese). Retrieved 2022-01-31.
  12. ^ a b "do Carmo, Manfredo P." TWAS. Retrieved 2022-01-31.
  13. ^ List of Fellows of the American Mathematical Society, retrieved 2015-01-13.
  14. ^ "Prizes and Awards". The World Academy of Sciences. 2016.
  15. ^ "Matemático Manfredo do Carmo morre aos 89 anos". Impa (in Portuguese). Retrieved 1 May 2018.
  16. ^ "Decease of Prof. Do Carmo | European Mathematical Society". euro-math-soc.eu. Retrieved 2022-01-31.
  17. ^ "News from the AMS". American Mathematical Society. Retrieved 2022-01-31.
  18. ^ do Carmo, M. P.; Warner, F. W. (1970-01-01). "Rigidity and convexity of hypersurfaces in spheres". Journal of Differential Geometry. 4 (2). doi:10.4310/jdg/1214429378. ISSN 0022-040X.
  19. ^ doCarmo, Manfredo P.; Lima, Elon (1969-05-01). "Isometric immersions with semi-definite second quadratic forms". Archiv der Mathematik. 20 (2): 173–175. doi:10.1007/BF01899010. ISSN 1420-8938.
  20. ^ Barbosa, João Lucas; do Carmo, Manfredo (1984-09-01). "Stability of hypersurfaces with constant mean curvature". Mathematische Zeitschrift. 185 (3): 339–353. doi:10.1007/BF01215045. ISSN 1432-1823.
  21. ^ Barbosa, J. Lucas; do Carmo, Manfredo; Eschenburg, Jost (1988-03-01). "Stability of hypersurfaces of constant mean curvature in Riemannian manifolds". Mathematische Zeitschrift. 197 (1): 123–138. doi:10.1007/BF01161634. ISSN 1432-1823.
  22. ^ Barbosa, J. L.; Carmo, M. Do (1976). "On the Size of a Stable Minimal Surface in R3". American Journal of Mathematics. 98 (2): 515–528. doi:10.2307/2373899. ISSN 0002-9327.
  23. ^ do Carmo, M.; Peng, C. K. (1979). "Stable complete minimal surfaces in 𝑅³ are planes". Bulletin of the American Mathematical Society. 1 (6): 903–906. doi:10.1090/S0273-0979-1979-14689-5. ISSN 0273-0979.
  24. ^ do Carmo, Manfredo; Xia, Changyu (2000-02-01). "Ricci curvature and the topology of open manifolds". Mathematische Annalen. 316 (2): 391–400. doi:10.1007/s002080050018. ISSN 1432-1807.
  25. ^ Barbosa, João Lucas; Carmo, Manfredo do (1978-10-01). "A proof of a general isoperimetric inequality for surfaces". Mathematische Zeitschrift. 162 (3): 245–261. doi:10.1007/BF01186367. ISSN 1432-1823.
  26. ^ Chern, S. S.; do Carmo, M.; Kobayashi, S. (1970), Browder, Felix E. (ed.), "Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length", Functional Analysis and Related Fields: Proceedings of a Conference in honor of Professor Marshall Stone, held at the University of Chicago, May 1968, Berlin, Heidelberg: Springer, pp. 59–75, doi:10.1007/978-3-642-48272-4_2, ISBN 978-3-642-48272-4, retrieved 2022-02-01
  27. ^ Carmo, Manfredo P. Do; Wallach, Nolan R. (1971). "Minimal Immersions of Spheres into Spheres". Annals of Mathematics. 93 (1): 43–62. doi:10.2307/1970752. ISSN 0003-486X.
  28. ^ do Carmo, Manfredo P.; Dajczer, Marcos (1982-01-01). "Helicoidal surfaces with constant mean curvature". Tohoku Mathematical Journal. 34 (3). doi:10.2748/tmj/1178229204. ISSN 0040-8735.
  29. ^ Carmo, M. Do; Dajczer, M. (1983). "Rotation Hypersurfaces in Spaces of Constant Curvature". Transactions of the American Mathematical Society. 277 (2): 685–709. doi:10.2307/1999231. ISSN 0002-9947.
  30. ^ Alencar, Hilário; do Carmo, Manfredo (1994). "Hypersurfaces with constant mean curvature in spheres". Proceedings of the American Mathematical Society. 120 (4): 1223–1229. doi:10.1090/S0002-9939-1994-1172943-2. ISSN 0002-9939.
  31. ^ Bérard, P.; do Carmo, M.; Santos, W. (1998-06-01). "Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature". Annals of Global Analysis and Geometry. 16 (3): 273–290. doi:10.1023/A:1006542723958. ISSN 1572-9060.
  32. ^ Barbosa, J. L. M.; Carmo, M. P. Do (2005-09-01). "On Stability of Cones in Rn+1 with Zero Scalar Curvature". Annals of Global Analysis and Geometry. 28 (2): 107–122. doi:10.1007/s10455-005-0039-5. ISSN 1572-9060.
  33. ^ "zbMATH Open - the first resource for mathematics". zbmath.org. Retrieved 2022-02-01.
  34. ^ do Carmo, Manfredo P. (2012). "Manfredo P. do Carmo – Selected Papers". doi:10.1007/978-3-642-25588-5. {{cite journal}}: Cite journal requires |journal= (help)
  35. ^ Shozo Motoyama, ed. (2004). Prelúdio para uma história: ciência e tecnologia no Brasil (in Portuguese). EdUSP. p. 358. ISBN 978-85-314-0797-0.
  36. ^ ":: CNPq - Prêmio Almirante Álvaro Alberto ::". www.premioalvaroalberto.cnpq.br. Retrieved 2022-02-01.
  37. ^ "Professor Manfredo P. Do Carmo will be awarded the honorary degree Doctor Honoris Causa by the Universidad de Murcia | European Mathematical Society". euro-math-soc.eu. Retrieved 2022-02-01.
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