Two characterizations of ellipsoidal cones

Details Two characterizations of ellipsoidal cones Two characterizations of ellipsoidal cones

2012-04-18

arxiv.org/abs/1204.3947v2

Mathematics

Metric Geometry

5 pages

Scientific paper

We give two characterizations of cones over ellipsoids. Let $C$ be a closed 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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