Sasaki, Takeshi; Yamada, Kotaro; Yoshida, Masaaki The hyperbolic Schwarz map for the hypergeometric equation. (English) Zbl 1157.33305 Exp. Math. 17, No. 3, 269-282 (2008). Summary: 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. Cited in 5 ReviewsCited in 4 Documents MSC: 33C05 Classical hypergeometric functions, \({}_2F_1\) 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:hypergeometric differential equation; Schwarz map; hyperbolic Schwarz map; flat surfaces; flat fronts × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid