Dual varieties and the duality of the second fundamental form

Tohsuke Urabe

Dual varieties and the duality of the second fundamental form

alg-geom 2008-02-03 v1 Algebraic Geometry

Authors: Tohsuke Urabe

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.

Keywords

Dual varieties Second fundamental form Compact real-analytic subvarieties Hyperbolic space

Cite

@article{arxiv.alg-geom/9702003,
  title  = {Dual varieties and the duality of the second fundamental form},
  author = {Tohsuke Urabe},
  journal= {arXiv preprint arXiv:alg-geom/9702003},
  year   = {2008}
}

Comments

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/

Dual varieties and the duality of the second fundamental form

Abstract

Keywords

Cite

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