Deformations of minimal surfaces. (English) Zbl 1040.53004

Mladenov, Ivaïlo M.; Angelov, Borislav

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1–10, 1999. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-1-7/pbk). 163-174 (2000).

Summary: We combine group-theoretical and differential-geometric techniques for considerations of minimal surface deformations in the ordinary three-dimensional space. This approach allows a consideration of a novel family of transformations generated by complex rotations. The resulting generalized deformations are compared with the well-known Bonnet and Goursat transformations and illustrated via a Schwarz skew quadrilateral to provide a clarification of their geometrical origin.
For the entire collection see [Zbl 0940.00039].

MSC:

53A10

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Keywords:

Bonnet and Goursat transformations; Schwarz skew quadrilateral