Totally Real Pseudo-umbilical Submanifolds In A Quasi-complex Projective Space CQ^n+p

In this thesis, we study some properties of the totally real pseudo-umbilical submanifolds Mn in a quasi-complex projective space CQn+p. By choosing a suit-able frame field, we estimate the Laplacian for the length square of the second fundamental form. Then we give some integral inequalities of Simons’type and improve some conclusions of the totally real pseudo-umbilical submanifolds in a quasi-complex projective space CQn. Finally, some rigidity theorems are obtained by some limitations.This thesis contains three chapters. In chapter 1, we introduce the theories about submanifolds, complex projective space, and the research status of complex projective space. In chapter 2, some basic knowledge is introduced such as the Rie-mannian manifolds, complex manifolds, and the submanifolds. In chapter 3, we study the submanifolds in a quasi-complex projective space CQn+p. In the end, we give a relevant lemma and prove the main conclusions.