Giovanni Battista Rizza
|Giovanni Battista Rizza|
February 7, 1924 |
Several complex variables
|Institutions||Università degli Studi di Genova
Istituto Nazionale di Alta Matematica
Sapienza University of Rome
Università degli Studi di Parma
|Alma mater||Università degli Studi di Genova|
|Doctoral advisor||Enzo Martinelli|
|Doctoral students||see the teaching activity section|
|Known for||Integral representation of pluriharmonic functions
Theory of functions on Algebras
|Notable awards||Premio Ottorino Pomini of the Unione Matematica Italiana (1954),
Golden medal "Benemeriti della Scuola, della Cultura, dell'Arte" (awarded by the President of the Italian Republic) (1973)
Giovanni Battista Rizza (born February 7, 1924) (at the registry office Giambattista Rizza) is an Italian mathematician, working in the fields of complex analysis of several variables and in differential geometry: he is known for his contribution to hypercomplex analysis, notably for extending Cauchy's integral theorem and Cauchy's integral formula to complex functions of a hypercomplex variable, the theory of pluriharmonic functions and for the introduction of the now called Rizza manifolds.
- 1 Biography
- 2 Work
- 3 Selected publications
- 4 See also
- 5 Notes
- 6 Biographical references
- 7 References
Life and academic career
Born in Piazza Armerina, the son of Giovanni and Angioletta Bocciarelli, he graduated from the Università degli Studi di Genova, earning his laurea degree in 1949 under the direction of Enzo Martinelli. In 1956 he was in Rome at the INdAM, having been awarded a scholarship for his early research activities. A year later, in 1957, he was elected "discepolo ricercatore" in the same institute. During the same year, he gave some lectures on topics belonging to the field of several complex variables, later included in the lecture notes (Severi 1958). In Rome he also met Lucilla Bassotti, who eventually become his wife. In 1961, he won the competitive examination for the chair of "Geometria analitica con elementi di Geometria Proiettiva e Geometria Descrittiva con Disegno" of the University of Parma, scoring first out of the three finalists: a year later, in 1962, he become extraordinary professor, and then, in 1965, ordinary professor to the same chair. In 1979 he become ordinary professor of "Geometria superiore", holding that chair uninterruptedly until 1994: from 1994 up to his retirement in 1997, he was "professore fuori ruolo" in the same department of mathematics where he worked for more than 35 years.
Apart from his research and teaching work, he was actively involved a as member of the editorial board of the "Rivista di Matematica della Università di Parma", and served also as the journal director from 1992 to 1997.
In 1954 he was awarded the Ottorino Pomini prize by the Unione Matematica Italiana, jointly with Gabriele Darbo: the judging commission was composed by Giovanni Sansone (as the president), Alessandro Terracini, Beniamino Segre, Giuseppe Scorza-Dragoni, Carlo Miranda, Mario Villa and Enzo Martinelli (as the secretary).
In 1973 He was awarded the golden medal "Benemeriti della Scuola, della Cultura, dell'Arte" by the President of the Italian Republic, as an acknowledgement his research and teaching and achievements as civil servant at the University of Parma.
In 1995, to celebrate his 70th birthday, an international conference on differential geometry was organized in Parma: the proceedings were later published as a special issue of the "Rivista di Matematica della Università di Parma".
Enzo Martinelli describes Giovanni Battista Rizza as a passionate researcher with a "strong intellectual force", and his scientific work as rich of geometrical ideas, denoting his strong algorithmic ability. According to Martinelli, Rizza is also a skilled organizer: his ability in organizational tasks is also acknowledged and praised by Schreiber (1973, p. 1), who also alludes the positive opinions of colleagues and students alike about his involvement in research, teaching and administrative duties at the mathematics department of the University of Parma.
Giovanni Battista Rizza has authored 53 research papers and 30 other scientific works, including research announcements, short notes, surveys and reports: he also wrote didactic notes and papers on historical topics, including commemorations of other scientists. His main fields of research are the theory of functions on algebras, the theory of functions of several complex variables, and differential geometry.
Theory of functions on algebras
The theory of functions on algebras, also referred to as hypercomplex analysis, is the study of functions whose domain is a subset of an algebra. The first works of Giovanni Battista Rizza belong to this field of research, and he was awarded the Premio Ottorino Pomini for his contributions.
where Γ1 is a 1-dimensional cycle homologous to zero, and also satisfying other technical conditions.
Few years later, he extended Cauchy's integral formula to every monogenic function F on a commutative normed real algebra A*, isomorphic to a given complex algebra A: precisely, he proves the formula
- X ≡ x* ≡ x identifies indifferently a point in the complex algebra A or in its isomorphic real algebra A*,
- Γ1 is again a 1-dimensional cycle homologous to zero, and satisfying other technical conditions,
- N(s) is the winding number of the cycle Γ1 respect to the zero divisor locus for the considered algebra.
Theory of analytic functions of several complex variables
All'estensione, tutt'altro che banale, allo spazio R2n dei metodi di Martinelli per dimostrare la (3), è dedicata una Memoria  di Giovanni Battista Rizza, il quale, sempre nell'ipotesi ρ(x1, y1,..., xn, yn) ∈ Cω, perviene a stabilire la (3) per n qualsiasi. Anche questo lavoro, per quanto redatto in lingua inglese e pubblicato su una delle principali riviste matematiche, non ha nella letteratura attuale, la notorietà che meriterebbe.
Rizza published only three work in this field: in the first one, the highly remarkable memoir (Rizza 1955), he extends to pluriharmonic functions of 2n real variables, n > 2, the methods introduced by Enzo Martinelli in order to give new proof of a result of Luigi Amoroso for pluriharmonic functions of four real variables. Precisely, he proves the following formula
- u is a polyharmonic function defined on a bounded domain Ω,
- ρ is a real analytic function defining the boundary of Ω by the equation
- Q(ρ) is a linear combination of the Levi forms of ρ relative to couples of complex variables,
- E is a linear tangential operator defined on ∂Ω.
Formula (1) express a condition the normal derivative of the boundary value of a pluriharmonic function on domain with real analytic boundary must satisfy. It can be used to costruct an integral representation for pluriharmonic functions on such kind of domains, by using the Green's formula for the Laplacian, and also to establish an integro-differential equation boundary values of pluriharmonic functions must satisfy. Rizza's result motivated other works on the same topic by Gaetano Fichera, Paolo de Bartolomeis and Giuseppe Tomassini.
During his teaching career at the University of Parma, Givanni Battista Rizza was the academic advisor of several students. A partial list of his studens includes the following ones:
- Rizza, Giovanni Battista (1950), "Sulle funzioni analitiche nelle algebre ipercomplesse", Pontificia Academia Scientiarum. Commentationes (in Italian) 14: 169–194, MR 57350. In "On analytic functions on hypercomplex algebras" (English translation of the title), Rizza extends the classical Cauchy's integral theorem to monogenic functions on a general complex algebra.
- Rizza, Giovanni Battista (1952), "Contributi al problema della determinazione di una formula integrale per le funzioni monogene nelle algebre complesse dotate di modulo e commutative", Rendiconti di Matematica, V Serie, (in Italian) 23 (1–2): 134–155, MR 0211370, Zbl 0047.32204. "Contributions to the problem of determining an integral formula for monogenic functions on complex commutative algebras with modulus" (English translation of the title).
- Rizza, Giovanni Battista (1952a), "Estensione della formula integrale di Cauchy alle algebre complesse dotate di modulo e commutative", Rendiconti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII, (in Italian), vol. XII (6): 667–669, MR 0062240, Zbl 0048.06101. "Extension of Cauchy's integral formula to commutative complex algebras with modulus" (English translation of the title).
- Rizza, Giovanni Battista (1953), "Teoria delle funzioni nelle algebre complesse dotate di modulo e commutative", Rendiconti di Matematica, V Serie, (in Italian) 23 (1–2): 221–249, MR 0211370, Zbl 0123.15203. "Function theory on commutative complex algebras with modulus" (English translation of the title).
- Rizza, Giovanni Battista (1954), "On Dirichlet's problem for components of analytic functions of several complex variables", Proceedings of the International Congress of Mathematicians, 1954. Volume II, ICM Proceedings, Amsterdam–Groningen: Erven P. Noordhoff N.V. / North-Holland Publishing Company, pp. 161–162. A short research announcement describing briefly the results proved in (Rizza 1955).
- Rizza, G. B. (1955), "Dirichlet problem for n-harmonic functions and related geometrical problems", Mathematische Annalen 130: 202–218, doi:10.1007/BF01343349, MR 0074881, Zbl 0067.33004, available at DigiZeitschirften.
- Rizza, G. B. (1957), "Su diverse estensioni dell’invariante di E. E. Levi nella teoria delle funzioni di più variabili complesse", Annali di Matematica Pura e Applicata (in Italian) 44 (1): 73–89, doi:10.1007/BF02415191, MR 0095965, Zbl 0091.25903. In the work "On different extensions of E. E. Levi invariant in the theory of functions of several complex variables" (English translation of the title), Rizza epitomizes all known extensions of the Levi invariant to hypersurfaces in ℂn for n > 2 in a single tensor of hybrid type. This paper is also interesting since it traces the story of such extensions back to the pioneering work of Eugenio Elia Levi.
- Rizza, G. B. (1958), "Appendice I. Rappresentazione esplicita di tipo integrale per le funzioni r–armoniche. Estensione al caso di r variabili complesse dell'invariante di E. E. Levi", in Severi, Francesco, Lezioni sulle funzioni analitiche di più variabili complesse – Tenute nel 1956–57 all'Istituto Nazionale di Alta Matematica in Roma (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp. 219–231, Zbl 0094.28002. The notes from the lectures given by Giovanni Battista Rizza for the course "Lectures on analytic functions of several complex variables", held by Francesco Severi at the Istituto Nazionale di Alta Matematica: the full course notes, published as a monograph, include also a chapter by Enzo Martinelli and an appendix by Mario Benedicty). The topics he exposes are summarized by the two parts of the title, whose English translations are "Explicit integral representation for –harmonic functions" and "Extension of the E. E. Levi invariant to the case of complex variables".
- Rizza, Giovanni Battista (1962a), "Finsler structures on almost complex manifolds", Proceedings of the International Congress of Mathematicians, Stockholm., ICM Proceedings, Stockholm. A short research announcement describing briefly the results proved in (Rizza 1963).
- Rizza, Giovanni Battista (1962b), "Strutture di Finsler sulle varietà quasi complesse", Rendiconti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII, (in Italian) 33 (5): 271–275. "Finsler structures on almost complex manifolds" (English translation of the title) is another short presentation of the results proved in (Rizza 1963).
- Rizza, Giovanni Battista (1963), "Strutture di Finsler di tipo quasi Hermitiano", Rivista di Matematica della Università di Parma, (2) (in Italian) 4: 83–106, MR 0166742, Zbl 0129.14101. The article giving the proofs of the results previously announced in references (Rizza 1962a) and Rizza (1962b): the English translation of the title reads as:-"Finsler structures of almost Hermitian type".
- Rizza, Giovanni Battista (1964), "F-forme quadratiche ed hermitiane", Rendiconti di Matematica, V Serie, (in Italian) 23 (1–2): 221–249, MR 0211370, Zbl 0123.15203. This article is the one Shoshichi Kobayashi cites as the first one in the theory of Rizza manifolds: an English translation of the title reads as:-"Hermitian and quadratic F-forms".
- Dentoni, Paolo; Rizza, Giovanni Battista (1972), "Una nuova classe di funzioni in un'algebra reale", Rendiconti dell'Istituto di Matematica dell'Università di Trieste (in Italian) 4: 171–181, MR 492318, Zbl Zbl 0251.30050. "A new class of functions on a real algebra" (English translation of the title) the authors introduce a new class of functions on a real algebra in the attempt of unifying the research trends on functions on real algebras in the seventies.
Historical, commemorative and survey papers
- Rizza, Giovanni Battista (12 December 1973), "Contributi recenti alla teoria delle funzioni nelle algebre", Rendiconti del Seminario Matematico e Fisico di Milano (in Italian) 43 (1): 45–54, doi:10.1007/BF02924838, MR 0350025, Zbl 0325.30040. "Recent contributions to the theory of functions on algebras" (English translation of the title) is a short but comprehensive survey paper detailing the works on the field done by Italian mathematicians during the years from 1961 to 1973: however, it also includes several biographical references to other earlier works by non Italian mathematicians and to historical bibliographies on hypercomplex analysis.
- Rizza, Giovanni Battista (1986), "Indirizzo di adesione", in Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; L.; Ciliberto, C.; Cimmino, G.; Cinquini, S.; De Giorgi, E.; Faedo, S.; Fichera, G.; Galligani, I.; Ghizzetti, A.; Graffi, D.; Greco, D.; Grioli, G.; Magenes, E.; Martinelli, E.; Pettineo, B.; Scorza, G.; Vesentini, E., Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei 77, Roma: Accademia Nazionale dei Lincei, pp. 29–30. The brief "participating address" presented to the International congress on the occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985), by Giovanni Battista Rizza on behalf of the University of Parma: the scientific relations between Leonida Tonelli and the Department of Mathematics in Parma are described.
- Rizza, Giovanni Battista (1984), "Enzo Martinelli: Scienziato e Maestro", Rivista di Matematica della Università di Parma, (4) (in Italian), 10*: 1–10, MR 0777308, Zbl 0557.01011. "Enzo Martinelli: Scientist and Master" (English translation of the title) is a celebrative paper written by Giovanni Battista Rizza to honor his former master.
- Rizza, Giovanni Battista (April 2002), "Commemorazione di Enzo Martinelli", Bollettino dell'Unione Matematica Italiana. Sezione A. La Matematica nella Società e nella Cultura, Serie VIII (in Italian) 5–A: 163–176, MR 1924344, Zbl 1194.01133. The "Commemoration of Enzo Martinelli" written by Rizza.
- Almost complex manifold
- Complex manifold
- Kähler manifold
- Pluriharmonic function
- Rizza manifold
- Several complex variables
- The detailed motivation for the award is reported in the Bollettino UMI 1954, pp. 477–478. The high scientific value of the works of the two young mathematicians induced the commission to ask the benefactors supporting the prize for a double award: their request was accepted.
- See the list of the recipients of the medal.
- See the list of the recipients of the medal "Benemeriti della Scuola, della Cultura, dell'Arte" and the Decreto ministeriale 17 febbraio 1999 conferring him the title of "Professor Emeritus".
- According to the motivation for the award of the "Premio Ottorino Pomini", reported on the Bollettino UMI (1954, p. 477), "Sono particolarmente degni di nota i risultati sui teoremi integrali per le funzioni regolari, sulle estensioni della formula integrale di Cauchy alle funzioni monogene sulle algebre complesse dotate di modulo commutative e sul conseguente sviluppo della relativa teoria, ed infine sulla struttura delle algebre di Clifford" ("Particularly notable results are the ones on the integral theorems for regular functions, the ones on the extension of Cauchy integral formula to complex commutative algebras with modulus, and lastly the ones on the structure of Clifford algebras").
- According to Martinelli (1994, p. 1), he was his first doctoral student.
- He, Giuseppe Arcidiacono and Dario Del Pasqua, were awarded the scholarship without sustaining the "colloquio" ("colloquium" in English translation), an oral exam where the candidate was asked to answer questions posed by a scientific jury, according to Roghi (2005, p. 46) who reports also an excerpt of the motivation given by the commission for the awarding of the scholarship to Rizza:-"...perché trattasi di giovani di cui è nota l'attività scientifica...", i.e. (English translation): "...because they are young researchers whose scientific activity is known, ...").
- Roghi (2005, pp. 8,29,277) also states that the scientific commission of the institute in charge in 1956 was still the first one, formed on 23 November 1939: its members were Francesco Severi (the president), Luigi Fantappie, Giulio Krall, Enrico Bompiani and Mauro Picone.
- "Disciple researcher" (English translation) was the appellation of junior research scientists working at the INdAM. See (Roghi 2005) for further details.
- See (Roghi 2005, p. 50).
- See (Roghi 2005, p. 50) and Severi (1958, p. III)
- See (Rizza 1958).
- Roghi (2005, p. 50) also precisely reports the costs carried by the INdAM to fund this course.
- "Analytic geometry with elements of projective geometry and descriptive geometry with drawing" (English translation).
- See the announce on the Bollettino UMI (1962, p. 454).
- See (Venturini 1963, p. 15).
- See the 1965 Yearbook of the University of Parma, p. 207: the exact date of this career advancement is 16th January 1965.
- Literally "higher geometry": it is an Italian university course on advanced geometry topics.
- See the 1980 Yearbook of the University of Parma, p. 209.
- See the 1995 Yearbook of the University of Parma, pp. 887 and 1036: the locution, literally meaning "out of role professor", identifies a nearly retired professor which is not in charge of any particular university course.
- According to the timeline of Editors in Chief of the "Rivista", as reported in the historical section of the journal web site.
- See (Schreiber 1973, p. 1).
- See (Donnini, Gigante & Mangione 1994). In the preface, the editors and members of the organizing committee briefly commemorate Franco Tricerri, former pupil of Rizza and speaker at the conference, who died in a plane crash in China few weeks before the proceedings of the conference were published (ibid., p. iii).
- According to Decreto ministeriale 17 febbraio 1999.
- See the list of members of the Balkan Society of Geometers (2011) and of the Tensor Society (2010).
- Martinelli (1994, p. 1) precisely characterizes Rizza's scientific work as developed with "...molta passione e forza intellettuale...", i.e. with (English translation) "...much passion and intellectual force...".
- Again according to Martinelli (1995, p. 2):-"Queste poche righe mi auguro siano servite a dimostrare che Rizza è un matematico ricco di idee geometriche e dotato di forti capacità algoritmiche.", i.e. (free English translation) "I hope those few lines have been of some help in demonstrating that Rizza is a mathematician rich of geometrical ideas and gifted with a strong algorithmic ability."
- See (Martinelli 1994, p. 2).
- See, for example, (Rizza 1984), (Rizza 1986) and (Rizza 2002).
- For more information see the survey article by Rizza (1973) and the references cited therein.
- See (Rizza 1950).
- See (Rizza 1952), (Rizza 1952a) and the survey (Rizza 1973).
- In the terminology of Rizza (1952, 1952a), the algebra A* is said to be the real image of (precisely, l'immagine reale di) A.
- (English translation): "To the far from trivial extension to the R2n space of Martinelli's methods is devoted a Memoir  of Giovanni Battista Rizza, who, again under the hypothesis ρ(x1, y1,..., xn, yn) ∈ Cω, succeeds in proving (3) for every n. And even this work, despite being written in English and published in a major mathematical journal, has not, in the current literature, the notoriety it deserves".
- The work (Rizza 1954) is only a research announcement related to the (Rizza 1955), while (Rizza 1958) is set of course notes based on the same paper and on (Rizza 1957).
- According to Fichera (1982b, p. 24), who praises this work as "molto considerevole": see also his comments in (Fichera 1982a, p. 135).
- See (Fichera 1982a, p. 135), (Fichera 1982b, pp. 24–25) and (Martinelli 1941).
- See (Fichera 1982a, p. 135), (Fichera 1982b, pp. 24–25) and (Fuks 1963, p. 277, footnote 1).
- See (Fichera 1982a, p. 134), (Fichera 1982b, p. 33) and (Martinelli 1941, p. 162).
- It is the Amoroso integro-differential equation: see (Fichera 1982a, p. 134) and (Fichera 1982b, pp. 33).
- See the hystorical survey sections in (Fichera 1982b, p. 25) and the work (de Bartolomeis & Tomassini 1981, p. 33).
- Balkan Society of Geometers (24 July 2011), The list of members of the Balkan Society of Geometers, retrieved April 19, 2011.
- Bollettino UMI (1954), "Notizie (Notices)", Bollettino dell'Unione Matematica Italiana, Serie III (in Italian) 9 (4): 467–490. The official relation of the judging commission for the awarding of the Ottorino Pomini Prize in 1954, jointly won by Gabriele Darbo and Giovanni Battista Rizza.
- Bollettino UMI (1962), "Notizie (Notices)", Bollettino dell'Unione Matematica Italiana, Serie III (in Italian) 17 (1): 120–157. The official announcement of the winning by Giovanni Battista Rizza of the chair of "Geometria analitica con elementi di Geometria Proiettiva e Geometria Descrittiva con Disegno" awarded by the University of Parma.
- The Editorial Board, ed. (1965), "Professori ordinari", Annuario dell'Università di Parma, A.A. 1964/1965, Parma: Università degli Studi di Parma.
- The Editorial Board, ed. (1980), "Professori ordinari", Annuario dell'Università di Parma, A.A. 1979/80, Parma: Università degli Studi di Parma.
- The Editorial Board, ed. (1995), "Professori ordinari", Annuario dell'Università di Parma, A.A. 1994/95, Parma: Università degli Studi di Parma.
- Martinelli, E. (1994), Donnini, S.; Gigante, G.; Mangione, V., eds., "Geometria differenziale – Analisi complessa. Convegno internazionale – Parma, 19–20 maggio 1994 in occasione del 70° compleanno di G. B. Rizza", Rivista di Matematica della Università di Parma, 5a Serie, (in Italian) 3 (I): 1–2
|chapter=ignored (help). "Homage to Giovanni Battista Rizza on his 70th birthday" (English translation of the title) a tribute to Giovanni Battista Rizza by his former master Enzo Martinelli.
- Il Ministro dell'Università e della Ricerca Scientifica e Tecnologica (19 February 1999), Decreto Ministeriale 17 Febbraio 1999 (in Italian). The "Ministerial Decree" awarding the title of "Professor Emeritus" to Giovanni Battista Rizza.
- Presidenza della Repubblica Italiana (July 31, 1973), Medaglia d'oro ai benemeriti della scuola della cultura e dell'arte: Giovanni Battista Rizza, retrieved May 31, 2011.
- Rivista di Matematica della Università di Parma, (the Editorial Board of) (12 December 2013), History, retrieved January 12, 2013.
- Roghi, G. (December 2005), "Materiale per una storia dell'Istituto Nazionale di Alta Matematica dal 1939 to 2003.", Bollettino della Unione Matematica Italiana, Sezione A, La Matematica nella Società e nella Cultura, Serie VIII (in Italian) 8–A (3, parte 2): x+301, MR 2225078, Zbl 1089.01500. "Materials toward a history of the Istituto Nazionale di Alta Matematica from 1939 to 2003" (English translation of title) is a monographic fascicle published on the "Bollettino della Unione Matematica Italiana", describing the history of the Istituto Nazionale di Alta Matematica Francesco Severi from its foundation in 1939 to 2003. It was written by Gino Roghi and includes a presentation by Salvatore Coen and a preface by Corrado De Concini. It is almost exclusively based on sources from the institute archives: the wealth and variety of materials included, jointly with its appendices and indexes, make this monograph a useful reference not only for the history of the institute itself, but also for the history of many mathematicians who taught, followed the institute courses or simply worked there.
- Schreiber, Bruno (1973), Curriculum Vitæ di Giambattista Rizza (in Italian), Istituto di Matematica dell'Università di Parma, p. 4. The official 1973 CV of Giovanni Battista Rizza, available from the Institute of Mathematics of the University of Parma.
- Tensor Society (2010), List of life members of the Tensor Society, retrieved 14 July 2013.
- Venturini, Giancarlo (1963), "Prolusione all'apertura dell'A.A. 1962/63", Annuario dell'Università di Parma, A.A. 1962/63, Parma: Università degli Studi di Parma. The opening address on the occasion of the beginning of the academic year 1962/63, given by the Magnifico Rettore prof. G. Venturini.
- Aikou, Tadashi (2004), "Finsler Geometry on Complex Vector Bundles", in Bao, David; Bryant, Robert L.; Chern, Shiing-Shen et al., A Sampler of Riemann–Finsler Geometry, Mathematical Sciences Research Institute Publications 50, Cambridge: Cambridge University Press, pp. 83–105, ISBN 0-521-83181-4, MR 2132658, Zbl 1073.53093 .
- de Bartolomeis, Paolo; Tomassini, Giuseppe (1981), "Traces of pluriharmonic functions", Compositio Mathematica 44 (1–3): 29–39, MR 662454, Zbl 0484.32007.
- Donnini, S.; Gigante, G.; Mangione, V., eds. (1994), "Geometria differenziale – Analisi complessa. Convegno internazionale – Parma, 19–20 maggio 1994 in occasione del 70° compleanno di G. B. Rizza", Rivista di Matematica della Università di Parma, Serie 5, 3 (Parte I). The proceedings of the international meeting "Differential Geometry – Complex analysis" held in Parma on May 19–20, 1994 to celebrate Giovanni Battista Rizza's 70th birthday, published by the Rivista di Matematica della Università di Parma. The first speaker was his former master Enzo Martinelli.
- Fichera, Gaetano (1982a), "Problemi al contorno per le funzioni pluriarmoniche", Atti del Convegno celebrativo dell'80° anniversario della nascita di Renato Calapso, Messina–Taormina, 1–4 aprile 1981 (in Italian), Roma: Libreria Eredi Virgilio Veschi, pp. 127–152, MR 0698973, Zbl 0958.32504. "Boundary value problems for pluriharmonic functions" (English translation of the title) deals with boundary value problems for pluriharmonic functions: Fichera gives a trace condition for the solvability of the problem and extensively reviews its history, starting from its beginning in the work of Henri Poincare and analyzing several earlier results of Enzo Martinelli, Giovanni Battista Rizza and Francesco Severi, as well as works of Aldo Andreotti among the others.
- Fichera, Gaetano (1982b), "Valori al contorno delle funzioni pluriarmoniche: estensione allo spazio R2n di un teorema di L. Amoroso", Rendiconti del Seminario Matematico e Fisico di Milano (in Italian) 52 (1): 23–34, doi:10.1007/BF02924996, MR 0802991, Zbl 0569.31006. In the work "Boundary values of pluriharmonic functions: extension to the space R2n of a theorem of L. Amoroso" (English translation of the title), Gaetano Fichera proves anothera trace condition for pluriharmonic functions and surveys other recent works in the fields, notably the one of de Bartolomeis & Tomassini (1981).
- Fuks, B. A. (1963), Introduction to the Theory of Analytic Functions of Several Complex Variables, Translations of Mathematical Monographs 8, Providence, RI: American Mathematical Society, pp. vi+374, MR 0168793, Zbl 0138.30902.
- Ichijyō, Yoshihiro (1988), "Finsler metrics on almost complex manifolds", Rivista di Matematica della Università di Parma, (IV) 14*: 1–28, MR 1045035, Zbl 0885.53031.
- Kobayashi, Shoshichi (1975), "Negative vector bundles and complex Finsler structures", Nagoya Mathematical Journal 57: 153–166, MR 0377126, Zbl 0326.32016. In this paper, Shoshichi Kobayashi acknowledges Giovanni Battista Rizza as the first one to study complex manifolds with Finsler structure, now called Rizza manifolds.
- Martinelli, Enzo (1941), "Studio di alcune questioni della teoria delle funzioni biarmoniche e delle funzioni analitiche di due variabili complesse coll’ausilio del calcolo differenziale assoluto", Atti della Reale Accademia d'Italia. Memorie della Classe di Scienze Fisiche, Matematiche e Naturali (in Italian) 12 (4): 143–167, JFM 67.0299.01, MR 0017810, Zbl 0025.40503. In "Study of some questions of the theory of biharmonic functions and of analytic functions of two complex variables by using the absolute differential calculus" (English translation of title) Martinelli proves an earlier result of Luigi Amoroso on the boundary values of pluriharmonic function by using tensor calculus.
- Scharnhorst, K. (2001), "Angles in Complex Vector Spaces", Acta Applicandae Mathematicae 69 (1): 95–103, doi:10.1023/A:1012692601098, MR 1868915, Zbl 0993.51010.
- Severi, Francesco (1958), Lezioni sulle funzioni analitiche di più variabili complesse – Tenute nel 1956–57 all'Istituto Nazionale di Alta Matematica in Roma (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp. XIV+255, Zbl 0094.28002. The "Lectures on analytic functions of several complex variables – Lectured in 1956–57 at the Istituto Nazionale di Alta Matematica in Rome" (English translation of the title) is a set of lecture notes from a course held by Francesco Severi at the Istituto Nazionale di Alta Matematica, including appendices of Enzo Martinelli, Giovanni Battista Rizza and Mario Benedicty.