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

1999/08/30 by Udo Hertrich-Jeromin · 1 citation
Mathematics · #math.DG #math.DS #msc:53A99

paper · pdf

published as manuscripta math. 102, 465-486 (2000) · 20 pages, plain TeX, 9 PostScript Figures

arxiv created 1999/08/30 · arxiv updated 2009/11/30

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.

Cited by

• Discrete minimal surfaces: Old and New

Related

• A discrete version of the Darboux transform for isothermic surfaces
• Discrete Isothermic Nets Based on Checkerboard Patterns
• Isothermic nets with spherical parameter lines from discrete holomorphic maps
• Discrete CMC surfaces in R³ and discrete minimal surfaces in S³. A discrete Lawson correspondence
• Minimal Darboux transformations