Abstract
The aim of the present paper is to study the delta-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting eta-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of delta-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and phi-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying (R) over bar.(S) over bar = 0, (P) over bar.(S) over bar = 0 is an eta-Einstein manifold. Moreover, we obtain the conditions for the eta-Lorentzian trans-Sasakian manifolds with a semi-symmetric-metric connection to be conformally flat and xi-conformally flat.