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2008 The Hyperbolic Schwarz Map for the Hypergeometric
Takeshi Sasaki, Kotaro Yamada, Masaaki Yoshida
Experiment. Math. 17(3): 269-282 (2008).


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.


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Takeshi Sasaki. Kotaro Yamada. Masaaki Yoshida. "The Hyperbolic Schwarz Map for the Hypergeometric." Experiment. Math. 17 (3) 269 - 282, 2008.


Published: 2008
First available in Project Euclid: 19 November 2008

zbMATH: 1157.33305
MathSciNet: MR2455700

Primary: 33C05 , 53C42

Keywords: flat fronts , flat surfaces , hyperbolic Schwarz map , Hypergeometric differential equation , Schwarz map

Rights: Copyright © 2008 A K Peters, Ltd.


Vol.17 • No. 3 • 2008
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