Abstract
The Schwarz map of the hypergeometric differential equation has been 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 hyperbolic 3-space. This map can be considered to be a lifting to 3-space of the Schwarz map. In this paper, we study the singularities of this map, and attempt to visualize its image when the monodromy group is a finite group or a typical Fuchsian group. General cases will be treated in forthcoming papers.
Citation
Takeshi Sasaki. Kotaro Yamada. Masaaki Yoshida. "The Hyperbolic Schwarz Map for the Hypergeometric." Experiment. Math. 17 (3) 269 - 282, 2008.
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