复射影空间中法丛平坦的全实伪脐子流形

数学物理学报

复射影空间中法丛平坦的全实伪脐子流形

张量; 宋卫东

安徽师范大学数学计算机科学学院芜湖 241000

收稿日期:2005-01-08 修回日期:2006-11-30 出版日期:2007-08-25 发布日期:2007-08-25
通讯作者: 张量
基金资助:
安徽省教育厅自然科学研究重点项目基金(2004kj166zd)、
安徽师范大学青年基金(2005xqn01)资助

Totally Real Pseudo-umbilical Submanifolds with Flat Normal Bundle of Complex Projective Space

Zhang Liang; Song Weidong

College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000

Received:2005-01-08 Revised:2006-11-30 Online:2007-08-25 Published:2007-08-25
Contact: Zhang Liang

摘要/Abstract

摘要： 该文证明了复射影空间中两种类型的法丛平坦全实伪脐子流形必是极小的,并在紧致的情形确定了它们的具体形状．此外,还说明了复射影空间中的全实全脐子流形一定不是法丛平坦的.

关键词: 复射影空间, 全实子流形, 伪脐子流形, 法丛平坦

Abstract: In this paper, the authors prove that two types of totally real pseudo-umbilical submanifolds with flat normal bundle must be minimal and determine their shapes under the circumstances that the submanifolds are compact. Moreover, the authors also show that the normal bundle of a totally real and totally umbilical submanifold can't be flat.

Key words: Complex projective space, Totally real submanifolds, Pseudo-umbilical submanifolds, Flat normal bundle

中图分类号:

53C40

张量; 宋卫东. 复射影空间中法丛平坦的全实伪脐子流形[J]. 数学物理学报, 2007, 27(4): 688-695.

Zhang Liang; Song Weidong.

Totally Real Pseudo-umbilical Submanifolds with Flat Normal Bundle of Complex Projective Space

[J]. Acta mathematica scientia,Series A, 2007, 27(4): 688-695.

[1]	尹松庭, 宋卫东. 复射影空间中具有平坦法丛的一般子流形[J]. 数学物理学报, 2011, 31(6): 1626-1632.
[2]	宋卫东. 关于具有平行第二基本形式的伪脐子流形[J]. 数学物理学报, 2000, 20(2): 158-162.