著者

Saji Kentaro Sasaki Takeshi Yoshida Masaaki

出版者

The Mathematical Society of Japan

雑誌

Journal of the Mathematical Society of Japan (ISSN:00255645)

巻号頁・発行日

vol.61, no.2, pp.559-578, 2009-04-01

被引用文献数

3

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The hyperbolic Schwarz map is defined in [SYY1] as a map from the complex projective line to the three-dimensional real hyperbolic space by use of solutions of the hypergeometric differential equation. Its image is a flat front ([GMM], [KUY], [KRSUY]), and generic singularities are cuspidal edges and swallowtail singularities. In this paper, for the two-parameter family of the confluent hypergeometric differential equations, we study the singularities of the hyperbolic Schwarz map, count the number of swallowtails, and identify the further singularities, except those which are apparently of type <I>A</I><SUB>5</SUB>. This describes creations/eliminations of the swallowtails on the image surfaces, and gives a stratification of the parameter space according to types of singularities. Such a study was made for a 1-parameter family of hypergeometric differential equation in [NSYY], which counts only the number of swallowtails without identifying further singularities.