ON 3-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO SEMI-SYMMETRIC METRIC CONNECTION

The aim of the present paper is to study 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Firstly, we prove that extended generalized M-projective phi-recurrent 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection is an eta-Einstein manifold with respect to Levi-Civita connection under some certain conditions. Later we study some curvature properties of 3-dimensional trans-Sasakian manifold admitting the above connection.