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Addendum to the paper: Sphere theorem by means of the ratio of mean curvature functions

Published online by Cambridge University Press:  25 July 2002

Sung-Eun Koh  and
Seung-Won Lee
Sung-Eun Koh
Affiliation:
Department of Mathematics, Konkuk University, Seoul, 143-701, Korea. e-mail: sekoh@kkucc.konkuk.ac.kr
Seung-Won Lee
Affiliation:
Department of Mathematics, Konkuk University, Seoul, 143-701, Korea. e-mail: sekoh@kkucc.konkuk.ac.kr
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Abstract

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It is shown that an immersion of n dimensional compact oriented manifold without boundary into the n+1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilic immersion if one of the mean curvature function H_l does not vanish and the ratio H_k/H_l is constant, 1\leq k, l \leq n, k\ne l.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 2 , May 2001 , pp. 275 - 276
Copyright
2001 Glasgow Mathematical Journal Trust

Footnotes

This research was supported by the KOSEF 1999-2-102-002-3.