CMC-1 Surfaces in Hyperbolic 3-space using the Bianchi-Calo method

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In this note we present a method for constructing CMC-1 surfaces in hyperbolic 3-space $\bfH^3(-1)$ in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by many years the modern approaches due to Bryant, Small and others. Besides its obvious historical interest, this note aims to complement Bianchi's analysis by deriving explicit formulae for CMC-1 surfaces and comparing the various approaches encountered in the literature.
13 pages, 4 figures

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Differential Geometry, History and Overview, 53A10

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http://salesiana.dossiersoluciones.com/handle/123456789/62297

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0110021
 http://arxiv.org/abs/math/0110021

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arXiv