• Title, Summary, Keyword: elliptic hyperboloid

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A CHARACTERIZATION OF ELLIPTIC HYPERBOLOIDS

  • Kim, Dong-Soo;Son, Booseon
    • Honam Mathematical Journal
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    • v.35 no.1
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    • pp.37-49
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    • 2013
  • 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.