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

Udo Hertrich-Jeromin·Emilio Musso·Lorenzo Nicolodi
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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.

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Udo Hertrich-Jeromin, Emilio Musso, Lorenzo Nicolodi. 1998-10-28. Moebius geometry of surfaces of constant mean curvature 1 in hyperbolic space. https://arxiv.org/abs/math/9810157

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