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Sphere theorem by means of the ratio of meancurvature functions

Published online by Cambridge University Press:  07 August 2001

Sung-Eun Koh
Sung-Eun Koh
Affiliation:
Department of Mathematics, Konkuk University, Seoul, 143-701, Korea Email: sekoh@kkucc.konkuk.ac.kr
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Abstract

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It is well known that a compact embedded hypersurface of the Euclidean space without boundary is a round sphere if one of mean curvature functions is constant. In this note, we show that a compact embedded hypersurface of the Euclidean space (and other constant curvature spaces) without boundary is a round sphere if the ratio of some two mean curvature functions is constant.

1991 Mathematics Subject Classification 53C40, 53C20.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 91 - 95
Copyright
2000 Glasgow Mathematical Journal Trust