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

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, t...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: De, Uday Chand, De, Krishnendu, S\ inem Güler
Format: Article
Language:English
Subjects:
Curvature
Fields (mathematics)
Manifolds (mathematics)
Solitary waves
Tensors
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2406.16108