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2017•Facta Universitatis Series Mathematics and InformaticsOpen access

ON ISOTROPIC RIEMANNIAN MANIFOLDS WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

Sezgi̇n Altay Demi̇rbağ

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Abstract

In this paper, we investigate some geometrical properties of Riemannian manifolds equipped with a semi-symmetric non-metric connection. First, it is proved that an isotropic Riemannian manifold with a semi-symmetric non-metric connection is Einstein. Then, it is shown that an isotropic Riemannian manifold admitting a proper concircular vector field with the above mentioned connection is a warped product. Moreover, the physical properties of a spacetime with a semi-symmetric non-metric connection are also investigated.

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What this paper is about

In this paper, we investigate some geometrical properties of Riemannian manifolds equipped with a semi-symmetric non-metric connection. First, it is proved that an isotropic Riemannian manifold with a semi-symmetric non-metric connection is Einstein. Then, it is shown that an isotropic Riemannian manifold admitting a proper concircular vector field with the above mentioned connection is a warped product. Moreover, the physical properties of a spacetime with a semi-symmetric non-metric connection are also investigated.

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Available abstract

In this paper, we investigate some geometrical properties of Riemannian manifolds equipped with a semi-symmetric non-metric connection. First, it is proved that an isotropic Riemannian manifold with a semi-symmetric non-metric connection is Einstein. Then, it is shown that an isotropic Riemannian manifold admitting a proper concircular vector field with the above mentioned connection is a warped product. Moreover, the physical properties of a spacetime with a semi-symmetric non-metric connection are also investigated.

Key concepts: Levi-Civita connection, Connection (principal bundle), Fundamental theorem of Riemannian geometry, Metric connection, Mathematics, Statistical manifold, Pseudo-Riemannian manifold, Metric (unit)

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