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

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.