Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts

Details Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts

2007-02-28

arxiv.org/abs/math/0702863v1

Mathematics

Classical Analysis and ODEs

15 pages, 12 figures

Scientific paper

In the previous paper (math.CA/0609196) we defined a map, called the hyperbolic Schwarz map, from the one-dimensional projective space to the three-dimensional hyperbolic space by use of solutions of the hypergeometric differential equation, and thus obtained closed flat surfaces belonging to the class of flat fronts. We continue the study of such flat fronts in this paper. First, we introduce the notion of derived Schwarz maps of the hypergeometric differential equation and, second, we construct a parallel family of flat fronts connecting the classical Schwarz map and the derived Schwarz map.

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