Abstract

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

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Jesús Jerónimo-Castro

Facultad de Ingenieria, Universidad Autónoma de Querétaro, Cerro de las Campanas s/n, C.P. 76010, Querétaro, México

Tyrrell B. McAllister

Dept. of Mathematics, University of Wyoming, Laramie, WY 82071, U.S.A.

tmcallis@uwyo.edu

Keywords

  • Ellipsoidal cone
  • centrally symmetric convex body

Mathematics Subject Classification

52A20, 53A07

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Suggested citation

J. Jerónimo-Castro, T. B. McAllister. “Two Characterizations of Ellipsoidal Cones.” Journal of Convex Analysis 20 (2013), No. 4, 1181–1187. https://doi.org/10.68381/jca20063

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.