Characterizations of a Lorentzian Manifold With a Semi-Symmetric Metric Connection

Abstract

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.