In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and sufficient condition is given. Furthermore, another condition is obtained when the convariant derivative of the projective invariant is kept.
We give pinching theorems with respect to the scalar curvatures of 4-dimensional projectively flat (concircularly flat、conharmonicly flat、quasiconformally flat)totally real minimal submanifolds in a 4-dimensional complex Projective Space.
