Abstract：Let CPn be an n -dimensio nal complex projective space with Fubini -Study metric of constant holomorphic sectional curvature 4 and Mn be a totally real submanifold in CPn .I f Mn is either umbilical in respect to mean curv ature vector field ξor minimal, then Mn is called a totally real pseudo -umbilical submanifo ld in CPn .In this paper , w e get sev eral propositions and theo rems about S , ξand H w hich are three important invariants in compact totally real pseudo -umbilical submanifold Mn .
