| On Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space |
| Received:March 02, 2006 Revised:October 12, 2006 |
| Key Words:
complex projective space totally real submanifolds pseudo-umbilical submanifolds parallel mean curvature vector.
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| Fund Project:the Natural Science Foundation of Anhui Educational Committee (No.KJ2008A05ZC); the Younger Teachers of Anhui Normal University (No.2005xqn01). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.02.024 |
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