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

Reference:

Hertrich-Jeromin, U., Musso, E. and Nicolodi, L., 2001. Möbius geometry of surfaces of constant mean curvature 1 in hyperbolic space. Annals of Global Analysis and Geometry, 19 (2), pp. 185-205.

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Official URL:

http://dx.doi.org/10.1023/A:1010738712475

Abstract

An overview of the various transformations of isothermic surfaces and their interrelations is given using aquaternionic formalism. Applications to the theory of cmc-1 surfaces inhyperbolic space are given and relations between the two theories are discussed. Within this context, we give Möbius geometric characterizations for cmc-1 surfaces in hyperbolic space and theirminimal cousins.

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