The Gauss map and the dual variety of real-analytic submanifolds in a sphere or in a hyperbolic space

Details The Gauss map and the dual variety of real-analytic submanifolds in a sphere or in a hyperbolic space The Gauss map and the dual variety of real-analytic submanifolds in a sphere or in a hyperbolic space

1995-07-09

arxiv.org/abs/alg-geom/9507008v3

Mathematics

Algebraic Geometry

AMSLaTeX v.1.2; This paper has been withdrawn by the author

Scientific paper

We study the Gauss map and the dual variety of a real-analytic immersion of a connected compact real-analytic manifold into a sphere or into a hyperbolic space. The dual variety is defined to be the set of all normal directions of the immersion. First, we show that the image of the Gauss map characterizes the manifold. Also we show that the dual variety characterizes the manifold. Besides, duality of the second fundamental form and some results on degeneration are obtained. In Algebraic Geometry E-prints eight files are tar-compressed and uuencoded.

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