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A Note of Isotropic Submanifolds with Constant Mean Curvature

YIN Songting1,2, SONG Weidong2   

  1. 1. Department of Basic Education, Tongling College, Tongling 244000, Anhui Province, China;2. College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui Province, China
  • Received:2007-06-28 Revised:1900-01-01 Online:2008-05-26 Published:2008-05-26
  • Contact: SONG Weidong

Abstract: Let Mn be an isotropic submanifold of Sn+p(c), constantH be mean curvature of Mn. Under the condition of equivalence of isotropic submanifolds and via divergence theorem, it is concluded that if the section curvature of Mn is not less than [n/2(n+1)](H2+c), then Mnis a totally umblilic submanifold or a Veronese submanifold in a totally umbilical hypersurface of Sn+p(c).

Key words: mean curvature, isotropic submanifolds, totally umbilic submanifolds

CLC Number: 

  • O186