Acta mathematica scientia, Series B >
RIGIDITY THEOREMS OF CLIFFORD TORUS
Received date: 2007-09-30
Revised date: 2008-05-05
Online published: 2010-05-20
Supported by
Project supported by the Foundation of Xuzhou Normal University (08XLA02) and the Education Department of Jiangsu Province (07KJB110115)
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, RicM ≤ 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}.
Key words： Principle curvatual; Ricci curvature; Clifford torus
ZHANG Yun-Tao . RIGIDITY THEOREMS OF CLIFFORD TORUS[J]. Acta mathematica scientia, Series B, 2010 , 30(3) : 890 -896 . DOI: 10.1016/S0252-9602(10)60086-0
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