Dual varieties and the duality of the second fundamental form

Abstract

First, we consider a compact real-analytic irreducible subvariety $M$ in a sphere and its dual variety $M^{\vee }$. We explain that two matrices of the second fundamental forms for both varieties $M$ and $M^{\vee }$ can be regarded as the inverse matrices of each other. Also generalization in hyperbolic space is explained.

LaTeX2e+AmsLaTeX. 3 pages. This manuscript was submitted to Proceedings of Symposium Real Analytic and Algebraic Singularities(IS(J held at Nagoya University in September - October, 1996. Adobe PDF version is available also at http://urabe-lab.math.metro-u.ac.jp/