Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A CHARACTERIZATION OF THE HYPERSPHERE

  • KIM, DONG-SOO (Department of Mathematics College of Natural Sciences Chonnam National University)
  • Received : 2005.04.07
  • Published : 2005.06.25
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Abstract

We study hypersurfaces in the Euclidean space with the following property: the tangential part of the position vector has constant length. As a result, we prove that among the connected and complete hypersurfaces in the Euclidean space, only the hypersphere centered at the origin satisfies the property.

Keywords

Acknowledgement

Supported by : Chonnam National University

References

  1. Soochow J. Math. v.27 no.4 Constant-ratio hypersurfaces Chen, B.Y.
  2. Beitrage Algebra Geom. v.44 no.1 More on convolution of Riemannian manifolds Chen, B.Y.
  3. Arch. Math. v.57 Hypersurfaces with a constant support function Hasanis, T.;Koutroufiotis, D.