Acta mathematica scientia,Series A

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The Rigidity of Clifford Torus {\boldmath Sm(\sqrt{\frac{m}{n}})\timesSn-m(\sqrt{\frac{n-m}{n}})

Zhang Yuntao ;Xu Senlin

  

  1. Department of Mathematics, Xuzhou Normal University, Xuzhou 220009
  • Received:2005-12-19 Revised:2006-11-30 Online:2008-02-25 Published:2008-02-25
  • Contact: Zhang Yuntao

Abstract: Let $M$ be an $n$-dimensional closed minimal hypersurface of the unit sphere $S^{n+1}(1)$. If $n \le S \le n+\frac{2}{3}$,then $S=n$ and $M$ is isometric to $S^m(\sqrt{m/n}) \times S^{n-m}(\sqrt{(n-m)/n})$.

Key words: Minimal hypersurface, Scalar curvature, Clifford torus

CLC Number: 

  • 53C40
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