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math.DG1999
Transformations of discrete isothermic nets and discrete cmc-1 surfaces in hyperbolic space
Udo Hertrich-Jeromin
Using a quaternionic calculus, the Christoffel, Darboux, Goursat, and spectral transformations for discrete isothermic nets are described, with their interrelations. The Darboux an…
math.DG1998
Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space
Udo Hertrich-Jeromin, Emilio Musso, Lorenzo Nicolodi
Various transformations of isothermic surfaces are discussed and their interrelations are analyzed. Applications to cmc-1 surfaces in hyperbolic space and their minimal cousins in…
math.DG1998
Orthogonal nets and Clifford algebras
Alexander I. Bobenko, Udo J. Hertrich-Jeromin
A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations f…