The objective of the present paper is to study of indefinite trans-Sasakian manifold with a semi-symmetric metric connection. We have found the relations between curvature tensors, Ricci curvature tensors and scalar curvature of indefinite trans-Sasakian manifolds with semi-symmetric metric connection and with metric connection. Also, we have proved some results on quasi-projectively flat and φ-projectively flat manifolds with respect to semi-symmetric metric connection. It is shown that the manifold satisfying R.S=0 is an η-Einstein manifold if α =0 and β =constant. It is also proved that the manifold satisfying P.S=0 is an η-Einstein manifold if α =0 and β =constant. Finally, we have obtained the conditions for the manifold with semi-symmetric metric connection to be conformally flat and ξ-conformally flat.

Tbilisi Mathematical Journal, Vol. 8(2) (2015), pp. 233-255