
Journal of Convex Analysis 20 (2013), No. 4, 11811187 Copyright Heldermann Verlag 2013 Two Characterizations of Ellipsoidal Cones Jesús JerónimoCastro 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 [Abstractpdf] We give two characterizations of cones over ellipsoids. Let $C$ be a closed convex linear cone in a finitedimensional 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. Keywords: Ellipsoidal cone, centrally symmetric convex body. MSC: 52A20, 53A07 [ Fulltextpdf (98 KB)] for subscribers only. 