Commentarii Mathematici Helvetici

, Volume 71, Issue 1, pp 60–69

The rigidity of Clifford torus\(S^1 \left( {\sqrt {\frac{1}{n}} } \right) \times S^{n - 1} \left( {\sqrt {\frac{{n - 1}}{n}} } \right)\)

  • Qing-Ming Cheng

DOI: 10.1007/BF02566409

Cite this article as:
Cheng, QM. Commentarii Mathematici Helvetici (1996) 71: 60. doi:10.1007/BF02566409


In this paper, we prove that ifM is ann-dimensional closed minimal hypersurface with two distinct principal curvatures of a unit sphereSn+1(1), thenS=n andM is a Clifford torus ifn≤S≤n+[2n2(n+4)/3(n(n+4)+4)], whereS is the squared norm of the second fundamental form ofM.

Copyright information

© Birkhäuser Verlag, Basel 1996

Authors and Affiliations

  • Qing-Ming Cheng
    • 1
  1. 1.Department of MathematicsSaga UniversitySagaJapan

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