Singularities of Blaschke normal maps of convex surfaces

Details Singularities of Blaschke normal maps of convex surfaces Singularities of Blaschke normal maps of convex surfaces

2010-01-08

arxiv.org/abs/1001.1200v3

Mathematics

Differential Geometry

5 pages Version 3; to appear in Comptes Rendus Mathematique

Scientific paper

10.1016/j.crma.2010.04.021

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.

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