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