Saddle tower

Two periods of a 3-fold 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

  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
This article is issued from Wikipedia - version of the 7/25/2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.