Convex Bodies with affinely equivalent projections and affine bodies of revolution

Luis Montejano

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Convex Bodies with affinely equivalent projections and affine bodies of revolution

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arxiv 2005.02290 v1 pith:QKVESEWE submitted 2020-05-05 math.MG

Convex Bodies with affinely equivalent projections and affine bodies of revolution

Luis Montejano This is my paper

classification math.MG

keywords bodiesconvexaffineaffinelyequivalentprojectionsrevolutionabstract

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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

Convex Bodies with affinely equivalent projections and affine bodies of revolution

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