Transformations of discrete isothermic nets and discrete cmc-1 surfaces in hyperbolic space
Abstract
Description
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
20 pages, plain TeX, 9 PostScript Figures