A characterization of round spheres

Author:
Sung-Eun Koh

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3657-3660

MSC (1991):
Primary 53C40, 53C42

MathSciNet review:
1469418

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Abstract: A new characterization of geodesic spheres in the simply connected space forms in terms of higher order mean curvatures is given: An immersion of an dimensional compact oriented manifold without boundary into dimensional Euclidean space, hyperbolic space or the open half sphere is a totally umbilic immersion if, for some the -th mean curvature does not vanish and the ratio is constant.

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Additional Information

**Sung-Eun Koh**

Affiliation:
Department of Mathematics, Kon-Kuk University, Seoul, 143-701, Korea

Email:
sekoh@kkucc.konkuk.ac.kr

DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04589-4

Keywords:
Higher order mean curvature,
principal curvature,
umbilical point,
Minkowski formula

Received by editor(s):
April 25, 1997

Additional Notes:
This research was supported by the KOSEF through Research Fund 96-0701-02-01-3, and by the Korean Ministry of Education through Research Fund BSRI-96-1438.

Communicated by:
Christopher Croke

Article copyright:
© Copyright 1998
American Mathematical Society