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http://dx.doi.org/10.5831/HMJ.2013.35.1.37

A CHARACTERIZATION OF ELLIPTIC HYPERBOLOIDS  

Kim, Dong-Soo (Department of Mathematics, Chonnam National University)
Son, Booseon (Department of Mathematics, Chonnam National University)
Publication Information
Honam Mathematical Journal / v.35, no.1, 2013 , pp. 37-49 More about this Journal
Abstract
Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.
Keywords
strictly convex hypersurface; elliptic hyperboloid; homogeneous extension; n-dimensional volume; elliptic cone; support function;
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1 Kim, D.-S. and Kim, Y. H., Some characterizations of spheres and elliptic paraboloids, Linear Algebra Appl. 437 (2012), no. 1, 113-120.   DOI   ScienceOn
2 Kim, D.-S. and Kim, Y. H., Some characterizations of spheres and elliptic paraboloids II, Linear Algebra Appl., 438 (2013), no. 3, 1356-1364.   DOI   ScienceOn
3 Kim, D.-S., Ellipsoids and elliptic hyperboloids in the Euclidean space $\mathbb{E}^{n+1}$, Submitted.
4 O'Neill, B., Elementary differential geometry, Revised second edition, Elsevier/Academic Press, Amsterdam, 2006.
5 Kim, D.-S. and Kim, Y. H., A characterization of ellipses, Amer. Math. Monthly 114 (2007), no. 1, 66-70.