Characterizations of a Lorentzian manifold with a semi-symmetric metric connection

In this article, we characterize a Lorentzian manifold M with a semisymmetric metric connection.At first, we consider a semi-symmetric metric connection whose curvature tensor vanishes and establish that if the associated vector field is a unit time-like torse-forming vector field, then M becomes a perfect fluid spacetime.Moreover, we prove that if M admits a semi-symmetric metric connection whose Ricci tensor is symmetric and torsion tensor is recurrent, then M represents a generalized Robertson-Walker spacetime.Also, we show that if the associated vector field of a semi-symmetric metric connection whose curvature tensor vanishes is a f -Ric vector field, then the manifold is Einstein and if the associated vector field is a torqued vector field, then the manifold becomes a perfect fluid spacetime.Finally, we apply this connection to investigate Ricci solitons.