Convex bodies with many elliptic sections

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Arelio, Isaac ; Montejano, Luis (2014)
  • Subject: Mathematics - Metric Geometry | 52A15, 53A04, 53A05

{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 $C^2$-differentiable boundary of a convex body also essentially characterize an ellipsoid.
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