Geodesic
Two Characterizations of Ellipsoidal Cones
Journal of convex analysis, Tome 20 (2013) no. 4, pp. 1181-1187

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 52A20, 53A07
Mots-clés : Ellipsoidal cone, centrally symmetric convex body 
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     author = {J. Jer\'onimo-Castro and T. B. McAllister},
     title = {Two {Characterizations} of {Ellipsoidal} {Cones}},
     journal = {Journal of convex analysis},
     pages = {1181--1187},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a15/}
}
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J. Jerónimo-Castro; T. B. McAllister. Two Characterizations of Ellipsoidal Cones. Journal of convex analysis, Tome 20 (2013) no. 4, pp. 1181-1187. http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a15/