复射影空间中具有平坦法丛的一般子流形

数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1626-1632.

复射影空间中具有平坦法丛的一般子流形

尹松庭|宋卫东

1.安徽铜陵学院数学与计算机系安徽铜陵 244000|
2.安徽师范大学数学与计算机科学学院安徽芜湖 241000

收稿日期:2011-03-18 修回日期:2011-11-26 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
安徽省教育厅自然科学研究重点项目(KJ2008A05ZC)和高等学校优秀青年人才资金项目(2011SQRL021ZD)资助

Generic Submanifolds with Flat Normal Bundle in a Complex Projective Space

YIN Song-Ting, SONG Wei-Dong

1.Department of Mathematics and Computer Science, Tongling College, Anhui |Tongling |244000;
2.College of Mathematics and Computer Science, Anhui Normal University, Anhui Wuhu 241000

Received:2011-03-18 Revised:2011-11-26 Online:2011-12-25 Published:2011-12-25

摘要/Abstract

摘要：

该文研究了复射影空间中具有平坦法丛一般子流形的曲率性质与几何性质之间的关系. 利用活动标架法, 得到关于截面曲率, Ricci曲率和第二基本形式模长的刚性定理, 推广和完善了已有文献的相关结果.

关键词: 复射影空间, 一般子流形, 平坦法丛

Abstract:

In this paper, the authors study the relation between properties on curvature and geometry of generic submanifolds with flat normal bundle in a complex projective space. By using the moving-frame method, the rigidity theorems on sectional curvature, Ricci curvature and the length of second fundamental form are obtained, which generalize and improve some results in the relevant literatures.

Key words: Complex projective space, Generic submanifold, Flat normal bundle

中图分类号:

53C40

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.

YIN Song-Ting, SONG Wei-Dong. Generic Submanifolds with Flat Normal Bundle in a Complex Projective Space[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1626-1632.