Many differential geometer studied different types of manifolds with a semi-symmetric metric connection. In this paper, we have considered a Riemannian manifold $(M^n,g)$, $(n>2)$, equipped with a semi-symmetric metric connection and studied the properties of the curvature tensor, the conformal curvature tensor, the Weyl projective curvature tensor and the conharmonic curvature tensor. We have also studied the Einstein spaces and recurrent space with respect to semi-symmetric metric connection and obtained certain results related to them.