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Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection by De, Uday Chand; De, Krishnendu; Güler, Sinem is a scholarly article available to read on EtoBox.

What is Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection about?

In this article, we characterize a Lorentzian manifold $\mathcal{M}$ with a semi-symmetric 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 $\mathcal{M}$ becomes a perfect fluid spacetime. Moreover, we prove that if $\mathcal{M}$ admits a semi-symmetric metric connection whose Ricci tensor is symmetric and torsion tensor is recurrent, then $\mathcal{M}$ 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.

Author

De, Uday Chand; De, Krishnendu; Güler, Sinem

Published

2024

Language

EN