拟复射影空间中的全实伪脐子流形

Totally Real Pseudo-umbilical Submanifolds in Quasi-complex Projective Space

利用活动标架法研究拟常曲率复射影空间中的全实伪脐子流形.通过计算第二基本形式模长平方的Laplacian,利用Stokes定理,得到了这类子流形的一个积分不等式及其刚性定理,使对全实伪脐子流形的研究由复射影空间扩展到伪复射影空间.

We studied the totally real pseudo-umbilical submanifolds in quasi-complex projective space by means of the method of moving frams. Based on the Stokes theorem and the Lapalacian of the square of the length of the second fundamental form,an integral inequality and a instrinsic rigidity theorem were obtained,which makes the study of the totally real pseudo-umbilical submanifolds extend from the complex projective to the quasi-complex projective.