Hypersurfaces  with  Constant  Mean Curvature  in  Space  Forms

数学季刊 ›› 1996, Vol. 11 ›› Issue (1): 42-48.

Hypersurfaces with Constant Mean Curvature in Space Forms

Henan University; Zhengzhou University;Henan University

收稿日期:1992-09-26 出版日期:1996-03-30 发布日期:2025-02-24
基金资助:
Supported by the National Natural Scicnce Fundations of China;Supportcd by the Natural Scicncc Fundations of Henan Education Committec.

Hypersurfaces with Constant Mean Curvature in Space Forms

Henan University; Zhengzhou University;Henan University

Received:1992-09-26 Online:1996-03-30 Published:2025-02-24
Supported by:
Supported by the National Natural Scicnce Fundations of China;Supportcd by the Natural Scicncc Fundations of Henan Education Committec.

摘要/Abstract

摘要： In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by asing the relationship between the square of the length of the second fundamental form and the mean curvature.We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval. This improved the relative results of M.Okumura,ShenYibihg and Sun Ziqi,etc.

关键词: , totally umbilical, second fundamental form, mean cur ature ,

Abstract: In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by asing the relationship between the square of the length of the second fundamental form and the mean curvature.We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval. This improved the relative results of M.Okumura,ShenYibihg and Sun Ziqi,etc.

Key words: , totally umbilical, second fundamental form, mean cur ature ,

中图分类号:

O177

宋鸿藻, 胡泽军, 胡聪娥. Hypersurfaces with Constant Mean Curvature in Space Forms[J]. 数学季刊, 1996, 11(1): 42-48.

Song Hongzao, Hu Zejun, Hu Congé. Hypersurfaces with Constant Mean Curvature in Space Forms[J]. Chinese Quarterly Journal of Mathematics, 1996, 11(1): 42-48.

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Hypersurfaces with Constant Mean Curvature in Space Forms

Hypersurfaces with Constant Mean Curvature in Space Forms

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