Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space
Differential Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/9810157,
title = {Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space},
author = {Udo Hertrich-Jeromin and Emilio Musso and Lorenzo Nicolodi},
journal= {arXiv preprint arXiv:math/9810157},
year = {2007}
}
Comments
18 pages, plain TeX, 8 PostScript figures