Research On Several Problems Of Totally Real Submanifolds In Quasi-complex Projective Space

In this thesis,we mainly consider some problems of totally real submanifolds in quasi-complex projective space and get a series of results.Firstly,we study the totally real submanifolds with parallel mean curvature in quasi-complex projective space by using the method of moving frame and self-adjoint operator.We have a series of integral inequalities.Secondly,we discuss the totally real submanifolds with method from flat in quasi-complex projective space and obtain an integral inequality.In particular,we not only give the properties of the totally real submanifolds with umbilical noral vector,but also prove that the totally real totally umbilical submanifolds in quasi-complex projective space is not method from flat.Finally,we investigate the problem of pseudo-umbilical submanifolds with 2-Harmonic in quasi-complex projective space and get an integral inequality and related corollaries.Furthermore,we obtain the condition that pseudo-umbilical submanifolds with 2-Harmonic is minimumal.