Hyperbolic Schwarz map for the hypergeometric differential equation
经典分析与常微分方程
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0609196,
title = {Hyperbolic Schwarz map for the hypergeometric differential equation},
author = {Takeshi Sasaki and Kotaro Yamada and Masaaki Yoshida},
journal= {arXiv preprint arXiv:math/0609196},
year = {2007}
}
备注
16 pages, 8 figures