On conformal curvature of a Riemannian manifold with a semi symmetric metric connection

In this thesis,it is studied on Riemannian manifolds with semi symmetric metric connection. In the first chapter, differentiable manifold, Riemannian manifold, affine connection, Riemannian connection , the covariant derivative of Riemannian manifold with respect to Riemannian connection are given. Then, the curvature tensors of Riemannian manifold are given and their properties of the curvature tensor are mentioned. Afterwards, the conformal curvature tensor of Riemannian manifold is obtained and properties of the conformal curvature tensor are given. In the second chapter, we study on Riemannian manifolds with semi symmetric metric connection. The connection coefficient of Riemannian manifold with semi-symmetric metric connnection is given and the curvature tensor of Rieannian manifold with semi-symmetric metric connection is obtained. In the third chapter, conformal curvature tensor of Riemannian manifold with semi-symmetric metric connection is given. After that, the properties of the conformal curvature tensor of semi symmetric metric connection are investigated. In the last part, properties of the tensor are mentioned and we proved that the conformal curvature tensor satisfies some relations.