Hyperbolic Schwarz map for the hypergeometric differential equation

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The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the singularities of this map, and visualize its image when the monodromy group is a finite group or a typical Fuchsian group. General cases will be treated in a forthcoming paper.
16 pages, 8 figures

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Classical Analysis and ODEs, 33C05, 53C42

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http://salesiana.dossiersoluciones.com/handle/123456789/124733

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609196
 http://arxiv.org/abs/math/0609196

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arXiv