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A CHARACTERIZATION OF ELLIPTIC HYPERBOLOIDS
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  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 1,  2013, pp.37-49
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.1.37
 Title & Authors
A CHARACTERIZATION OF ELLIPTIC HYPERBOLOIDS
Kim, Dong-Soo; Son, Booseon;
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 Abstract
Consider a non-degenerate open convex cone C with vertex the origin in the 2-dimensional Euclidean space . 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 is independent of the point , 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;
 Language
English
 Cited by
1.
Center of Gravity and a Characterization of Parabolas, Kyungpook mathematical journal, 2015, 55, 2, 473  crossref(new windwow)
2.
Revisiting floating bodies, Expositiones Mathematicae, 2016  crossref(new windwow)
3.
Areas associated with a Strictly Locally Convex Curve, Kyungpook mathematical journal, 2016, 56, 2, 583  crossref(new windwow)
 References
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2.
Kim, D.-S. and Kim, Y. H., Some characterizations of spheres and elliptic paraboloids, Linear Algebra Appl. 437 (2012), no. 1, 113-120. crossref(new window)

3.
Kim, D.-S. and Kim, Y. H., Some characterizations of spheres and elliptic paraboloids II, Linear Algebra Appl., 438 (2013), no. 3, 1356-1364. crossref(new window)

4.
Kim, D.-S., Ellipsoids and elliptic hyperboloids in the Euclidean space $\mathbb{E}^{n+1}$, Submitted.

5.
O'Neill, B., Elementary differential geometry, Revised second edition, Elsevier/Academic Press, Amsterdam, 2006.