and M be an n-dimensional complete totally real space-like submanifold isometrically immersed in Nn (c).

We deduce the Riemannian metric on complex projective space from Riemannian submersion π:S2n+1→CPn,get its volume element We also prove that one type totally real submanifolds of CPn is none but ndimensional sphere Sn.

This dissertatian is mainly concernd with several problems of Kaehler submanifolds and totally real submanifolds in complex projective space.

In this thesis,we study several problems of Kaehler submanifolds and totally real submanifolds in a locally symmetric Bochner-Kaehler manifold.

In this paper, we consider complete space like submanifolds of a pseudo Riemannian space of constant curvature, the result of Toru Ishihara is generalized.

Complete space-like submanifolds with parallel mean curvature vector in de Sitter spaces

It is proved that if an n-dimensional compact space-like submanifold immersed in de Sitter space satisfies some condition,then Yang-Mills fields is vanishing.

This paper discusses the space-like submanifolds with constant mean curvature in a pseudo-Riemannian space form,and obtain an integrate inequality and a rigidity theorem.

In this paper, we obtain a complete solution to a pinching problem for the ricci curva-ture of totally real minimal submanifolds in a locally symmetric Bochner-Kaehler manifold.

By employing the method of [1,5],we give some Laplacian eigenvalue inequalities for compact totally real minimal submanifolds in a complex projective space with the holomorphic first normal space.