Singularities of Blaschke normal maps of convex surfaces
Differential Geometry
2010-05-12 v3
Abstract
We prove that the difference between the numbers of positive swallowtails and negative swallowtails of the Blaschke normal map for a given convex surface in affine space is equal to the Euler number of the subset where the affine shape operator has negative determinant.
Keywords
Cite
@article{arxiv.1001.1200,
title = {Singularities of Blaschke normal maps of convex surfaces},
author = {Kentaro Saji and Masaaki Umehara and Kotaro Yamada},
journal= {arXiv preprint arXiv:1001.1200},
year = {2010}
}
Comments
5 pages Version 3; to appear in Comptes Rendus Mathematique