Some properties of three dimensional trans-Sasakian manifolds with a semi-symmetric metric connection

Abstract

In this paper we have studied ξ-projectively flat 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Next, we have shown a skew-symmetric property of projective Ricci-tensor with respect to semi-symmetric metric connection in a 3-dimensional trans-Sasakian manifold. Then we have proved quasi-projectively flat, ϕ-projectively flat 3-dimensional trans-Sasakian manifold with semi-symmetric metric connection. In the last section we have shown an example of a three dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection.