Saddle tower

In differential geometry, a saddle tower is a minimal surface family generalizing the singly periodic Scherk's second surface so that it has N-fold (N > 2) symmetry around one axis. ^[1]^[2]

These surfaces are the only properly embedded singly periodic minimal surfaces in R³ with genus zero and ﬁnitely many Scherk-type ends in the quotient. ^[3]

Images

http://archive.msri.org/about/sgp/jim/geom/minimal/library/saddletower/main.html

References

^ H. Karcher, Embedded minimal surfaces derived from Scherk's examples, Manuscripta Math. 62 (1988) pp. 83–114.
^ H. Karcher, Construction of minimal surfaces, in "Surveys in Geometry", Univ. of Tokyo, 1989, and Lecture Notes No. 12, SFB 256, Bonn, 1989, pp. 1–96.
^ Joaquın Perez and Martin Traize, The classiﬁcation of singly periodic minimal surfaces with genus zero and Scherk-type ends, Transactions of the American Mathematical Society, Volume 359, Number 3, March 2007, Pages 965–990

[1] H. Karcher, Embedded minimal surfaces derived from Scherk's examples, Manuscripta Math. 62 (1988) pp. 83–114.

[2] H. Karcher, Construction of minimal surfaces, in "Surveys in Geometry", Univ. of Tokyo, 1989, and Lecture Notes No. 12, SFB 256, Bonn, 1989, pp. 1–96.

[3] Joaquın Perez and Martin Traize, The classiﬁcation of singly periodic minimal surfaces with genus zero and Scherk-type ends, Transactions of the American Mathematical Society, Volume 359, Number 3, March 2007, Pages 965–990

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