Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space

Details Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space

1998-10-28

arxiv.org/abs/math/9810157v1

Ann. Global Anal. Appl. 19, 185-205 (2001)

Mathematics

Differential Geometry

18 pages, plain TeX, 8 PostScript figures

Scientific paper

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 Euclidean space are presented: the Umehara-Yamada perturbation, the classical and Bryant's Weierstrass type representations, and the duality for cmc-1 surfaces are interpreted in terms of transformations of isothermic surfaces. A new Weierstrass type representation is introduced and a Moebius geometric characterization of cmc-1 surfaces in hyperbolic space and minimal surfaces in Euclidean space is given.

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