Editorial Board

JMI2010B-6 A Darboux transformation for discrete s-isothermic surfaces (pp.157-169)

Author(s): Tim Hoffmann

J. Math-for-Ind. 2B (2010) 157-169.

We give an overview on the discretization of isothermic surfaces, with special emphasis on the so-called s-isothermic surfaces, which are in some sense a nonlinear deformation of the classical discrete isothermic surfaces. For s-isothermic surfaces we give a way to define surfaces of constant mean curvature (cmc surfaces for short) without actually defining an a priori notion of curvature itself. We will compute discrete versions of rotational symmetric cmc surfaces (Delaunay surfaces) as an example. Finally, we give a discrete equivalent of the Sinh-Gordon equation, solutions of which describe---in complete analogy to the smooth case---discrete s-isothermic cmc surfaces.

Keyword(s).  mathematics, discrete differential geometry, s-isothermic nets, constant mean curvature