Singularities of Blaschke normal maps of convex surfaces

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.

arXiv comment5 pages Version 3; to appear in Comptes Rendus Mathematique

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