复射影空间CP n+p2中具有2-调和的一般子流形

摘要

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 pro jective space.%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。