Deformations of Minimal Surfaces

Abstract

Here 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 the Schwarz skew quadrilateral to provide a clarification of their geometrical origin.