Chinese Quarterly Journal of Mathematics ›› 2013, Vol. 28 ›› Issue (2): 202-205.

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A Note of the Hyperovaloid Characterization

  

  1. Department of Mathematics, Sichuan University

  • Received:2011-09-19 Online:2013-06-30 Published:2023-03-01
  • About author:WANG Bao-fu(1965-), male, native of Dongtai, Jiangsu, a professor of Sichuan University, engages in differential geometry; SHENG Li(1979-), male, native of Shihezi, Xinjiang, a lecturer of Sichuan University, engages in differential geometry.
  • Supported by:
    Supported by the NSFC(11171235,11201318)

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Abstract: Let Lr be the r-th affine mean curvature of a hyperovaloid in A n+1 , in this paper, we prove that if Lr=0 and for some fixed 1 ≤i1< ···< ir<n,...= C everywhere on M, then M must be an ellipsoid, where C is a constant.

Key words: a?ne mean curvature, hyperovaloid, ellipsoid

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