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Archiv der Mathematik

, Volume 88, Issue 2, pp 181–192 | Cite as

Convex bodies with equiframed two-dimensional sections

  • Nico Düvelmeyer
Article
  • 45 Downloads

Abstract.

We show that a centred, convex body in \({\mathbb{R}^{d}}\) (d ≥ 3) all of whose two-dimensional sections through the origin are equiframed is an ellipsoid.

Mathematics Subject Classification (2000).

52A15 52A20 52A21 46B20 46C15 

Keywords.

Birkhoff orthogonality equiframed curves Euclidean space inner product space Radon curves 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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