RIGIDITY THEOREMS OF CLIFFORD TORUS

doi:10.1016/S0252-9602(10)60086-0

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 890-896.doi: 10.1016/S0252-9602(10)60086-0

RIGIDITY THEOREMS OF CLIFFORD TORUS

张运涛

Department of Mathematics, Xuzhou Normal University, Xuzhou |220009, China

收稿日期:2007-09-30 修回日期:2008-05-05 出版日期:2010-05-20 发布日期:2010-05-20
基金资助:
Project supported by the Foundation of Xuzhou Normal University (08XLA02) and the Education Department of Jiangsu Province (07KJB110115)

RIGIDITY THEOREMS OF CLIFFORD TORUS

ZHANG Yun-Tao

Department of Mathematics, Xuzhou Normal University, Xuzhou |220009, China

Received:2007-09-30 Revised:2008-05-05 Online:2010-05-20 Published:2010-05-20
Supported by:
Project supported by the Foundation of Xuzhou Normal University (08XLA02) and the Education Department of Jiangsu Province (07KJB110115)

摘要/Abstract

摘要：

In this article, we prove that the Clifford torus S¹(√1-r²) ×Sⁿ^-1(r) is the only closed hypersurface in the unit sphere Sⁿ⁺¹(1) with infinite fundamental group, which satisfy r²≥(n-1)/n, Ric_M ≤ C_-(H), and S ≤ S₊(H). Moreover, we give a characterization of Clifford torus S¹(√1-r²) ×Sⁿ^-1(r) with r² ={2(n-1)+nH²±|H|√n²H²+4(n-1)/2n(1+H²}.

关键词: Principle curvatual, Ricci curvature, Clifford torus

Abstract:

Key words: Principle curvatual, Ricci curvature, Clifford torus

中图分类号:

53C42

张运涛. RIGIDITY THEOREMS OF CLIFFORD TORUS[J]. 数学物理学报(英文版), 2010, 30(3): 890-896.

ZHANG Yun-Tao. RIGIDITY THEOREMS OF CLIFFORD TORUS[J]. Acta mathematica scientia,Series B, 2010, 30(3): 890-896.

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RIGIDITY THEOREMS OF CLIFFORD TORUS

RIGIDITY THEOREMS OF CLIFFORD TORUS

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