| 摘要: |
| 本文研究了复射影空间中具有2-调和的一般子流形问题.利用活动标架法,获得了这类子流形成为极小子流形的Pinching定理和Simons型积分不等式,此外还得到关于2-调和伪脐一般子流形的一个刚性定理,推广了复射影空间中具有2-调和全实子流形的一些相应结果. |
| 关键词: 复射影空间 一般子流形 2-调和 伪脐 平行平均曲率 全测地 |
| DOI： |
| 分类号:O186.16 |
| 基金项目:安徽省教育厅自然科学重点项目(KJ2010A125);安徽省高等学校优秀青年人才基金项目(2011SQRL021ZD);安徽省高等学校省级自然科学资金项目(KJ2012B197). |
|
| GENERIC SUBMANIFOLDS WITH 2-HARMONIC IN A COMPLEX PROJECTIVE SPACE |
|
FAN Sheng-xue1, SONG Wei-dong2
|
|
1.Tongda College, Nanjing University of Posts & Telecommunications, Yangzhou 225127, China;2.College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China
|
| Abstract: |
| In this paper, the authors study the generic submanifolds with 2-Harmonic in a complex projective space. By method of moving frame, we obtain a pinching theorems of generic submanifolds is minimal and a promotion of J. Simons' type integral inequality. Moreover, the authors also obtain some rigidity theorems of the generic submanifolds with 2-Harmonic and psedu-umbilical and improve the results of the totally real submanifolds with 2-Harmonic in a complex projective space. |
| Key words: complex projective space generic submanifolds 2-harmonic psedu-umbilical parallel mean curvature totally geodesic |
