Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (3): 890-896.doi: 10.1016/S0252-9602(10)60086-0

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RIGIDITY THEOREMS OF CLIFFORD TORUS

 ZHANG Yun-Tao   

  1. 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)

Abstract:

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)/nRicM ≤ 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

CLC Number: 

  • 53C42
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