关于复射影空间中的全实伪脐子流形

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

中文关键词:  复射影空间  全实子流形  伪脐子流形  平行平均曲率向量.

英文关键词:complex projective space  totally real submanifolds  pseudo-umbilical submanifolds  parallel mean curvature vector.

中文摘要:

      设$M^n$是复射影空间${\bf C}P^{n+p}$中的全实子流形. 本文研究$M^n$的平行脐性法向量场在法丛中的位置. 在$p>0$的情形通过选取合适的标架场, 得到具有平行平均曲率向量的全实伪脐子流形关于第二基本形式模长平方的一个Pinching定理.

英文摘要:

      Let $M^n$ be a totally real submanifold in a complex projective space ${\bf C}P^{n+p}$. 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.