paper

Transformations of discrete isothermic nets and discrete cmc-1 surfaces in hyperbolic space

arXiv:math/9908161

Abstract

Using a quaternionic calculus, the Christoffel, Darboux, Goursat, and spectral transformations for discrete isothermic nets are described, with their interrelations. The Darboux and spectral transformations are used to define discrete analogs for cmc-1 surfaces in hyperbolic space and to obtain a discrete version of Bryant's Weierstrass type representation.

20 pages, plain TeX, 9 PostScript Figures

Transformations of discrete isothermic nets and discrete cmc-1 surfaces in hyperbolic space · wovepaper