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

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

1999-08-30

arxiv.org/abs/math/9908161v1

manuscripta math. 102, 465-486 (2000)

Mathematics

Differential Geometry

20 pages, plain TeX, 9 PostScript Figures

Scientific paper

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.

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