| 关于复射影空间中的全实伪脐子流形 |
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| 引用本文： | 张量. 关于复射影空间中的全实伪脐子流形[J]. 数学研究及应用, 2008, 28(2): 421-428. DOI: 10.3770/j.issn.1000-341X.2008.02.024 |
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| 作者姓名： | 张量 |
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| 作者单位： | 安徽师范大学数学计算机科学学院, 安徽 芜湖 241000 |
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| 基金项目： | 安徽省自然科学基金 , 安徽师范大学校科研和教改项目 |
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| 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.
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| 关 键 词： | complex projective space totally real submanifolds pseudo-umbilical submanifolds parallel mean curvature vector. 复射影空间 全实伪脐子流形 Projective Space Complex Submanifolds square length the second fundamental form parallel mean curvature vector case pinching theorem frame vector field study position umbilical normal bundle paper |
| 收稿时间： | 2006-03-02 |
| 修稿时间： | 2006-03-02 |
On Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space |
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| ZHANG Liang. On Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space[J]. Journal of Mathematical Research with Applications, 2008, 28(2): 421-428. DOI: 10.3770/j.issn.1000-341X.2008.02.024 |
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| Authors: | ZHANG Liang |
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| Affiliation: | College of Mathematics and Computer Science,Anhui Normal University,Anhui 241000,China |
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| Abstract: | Let Mn be a totally real submanifold in a complex projective space CPn p.In this paper,we study the position of the parallel umbilical normal vector field of Mn 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. |
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| Keywords: | complex projective space totally real submanifolds pseudo-umbilical submanifolds parallel mean curvature vector. |
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