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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