Abstract

We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the C2C^2-differentiable boundary of a convex body also essentially characterize an ellipsoid.

Author information

Contact details are reproduced from the original publication and may be historical.

Isaac Arelio

Instituto de Matemáticas UNAM, Circuito Ext. Cd. Universitaria, Colonia Copilco el Bajo, México D.F. - C.P. 04510

incordio@im.unam.mx

Luis Montejano

Instituto de Matemáticas UNAM, Circuito Ext. Cd. Universitaria, Colonia Copilco el Bajo, México D.F. - C.P. 04510

luis@matem.unam.mx

Keywords

  • Convex surface
  • quadric surface
  • quadric curve
  • planar section
  • characterization of ellipsoid

Mathematics Subject Classification

52A15, 53A04, 53A05

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Suggested citation

I. Arelio, L. Montejano. “Convex Bodies with Many Elliptic Sections.” Journal of Convex Analysis 24 (2017), No. 2, 685–693. https://doi.org/10.68381/jca24043

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.