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arXiv · 2005.02290

Convex Bodies with affinely equivalent projections and affine bodies of revolution

Luis Montejano
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Abstract

Abstract In this paper, we study affine bodies of revolution. This will allow us to prove that a convex body all whose orthogonal $n$-projections are affinely equivalent is an ellipsoid, provided $n\equiv 0,1, 2$ mod $4$, $n>1$ with the possible exemption of $n=133$. Our proof uses convex geometry and topology of compact Lie groups. AMS classification subject: 22E10, 52A05

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Luis Montejano. 2020-05-05. Convex Bodies with affinely equivalent projections and affine bodies of revolution. https://arxiv.org/abs/2005.02290

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