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]

Two periods of a 3-fold saddle tower.

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

The Saddle Tower Surface Families

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

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[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