Abstract

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 ≡ 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.

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Keywords

  • Affinelly equivalent projections
  • bodies of revolution
  • ellipsoids

Mathematics Subject Classification

52A20, 52A21, 22E15

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Suggested citation

L. Montejano. “Convex Bodies with Affinely Equivalent Projections and Affine Bodies of Revolution.” Journal of Convex Analysis 28 (2021), No. 3, 871–877. https://doi.org/10.68381/jca28050

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press.