On Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space  

作　　者：ZHANG Liang 

机构地区：[1]College of Mathematics and Computer Science, Anhui Normal University, Anhui 241000, China

出　　处：《Journal of Mathematical Research and Exposition》2008年第2期421-428,共8页数学研究与评论（英文版）

基　　金：Foundation item： the Natural Science Foundation of Anhui Educational Committee （No. KJ2008A05ZC）; the Younger Teachers of Anhui Normal University （No. 2005xqn01）.

摘　　要：Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.Let M^n be a totally real submanifold in a complex projective space CP^n＋p.In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p〉0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.

关 键 词：complex projective space totally real submanifolds pseudo-umbilical submanifolds parallel mean curvature vector 

分 类 号：O186.12[理学—数学]