Riemannian manifold admitting a new type of semi-symmetric metric connection

Abstract

We define a new type of semi-symmetric metric connection on a Riemannian manifold and established its existence. Further, we find some basic results of curvature tensor and Ricci tensor. It is proved that such connection on a Riemannian manifold is conformally invariant under certain conditions. We also studied some properties of concircular curvature tensor of the Riemannian manifolds with respect to the semisymmetric metric connection ̅. To validate our findings, we construct a non-trivial example of 3- dimensional Riemannian manifold equipped with a semi-symmetric metric connection ̅.