The Hyperbolic Schwarz Map for the Hypergeometric
Sasaki, Takeshi ; Yamada, Kotaro ; Yoshida, Masaaki
Experiment. Math., Tome 17 (2008) no. 1, p. 269-282 / Harvested from Project Euclid
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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.
Publié le : 2008-05-15
Classification:  hypergeometric differential equation,  Schwarz map,  hyperbolic Schwarz map,  flat surfaces,  flat fronts,  33C05,  53C42 
@article{1227121382,
     author = {Sasaki, Takeshi and Yamada, Kotaro and Yoshida, Masaaki},
     title = {The Hyperbolic Schwarz Map for the Hypergeometric},
     journal = {Experiment. Math.},
     volume = {17},
     number = {1},
     year = {2008},
     pages = { 269-282},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1227121382}
}

Sasaki, Takeshi; Yamada, Kotaro; Yoshida, Masaaki. The Hyperbolic Schwarz Map for the Hypergeometric. Experiment. Math., Tome 17 (2008) no. 1, pp.  269-282. http://gdmltest.u-ga.fr/item/1227121382/