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arXiv · 1204.3947

Two characterizations of ellipsoidal cones

Jesús Jerónimo-Castro·Tyrrell B. McAllister
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Abstract

We give two characterizations of cones over ellipsoids. Let $C$ be a closed pointed convex linear cone in a finite-dimensional real vector space. We show that $C$ is a cone over an ellipsoid if and only if the affine span of $\partial C \cap \partial(a - C)$ has dimension $\dim(C) - 1$ for every point $a$ in the relative interior of $C$. We also show that $C$ is a cone over an ellipsoid if and only if every bounded section of $C$ by an affine hyperplane is centrally symmetric.

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Jesús Jerónimo-Castro, Tyrrell B. McAllister. 2012-04-18. Two characterizations of ellipsoidal cones. https://arxiv.org/abs/1204.3947

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