A parallel vector field on Riemannian manifolds admitting semi-symmetric non-metric connection

Abstract

In this paper, we study Riemannian manifolds admitting a type of semi-symmetric non-metric connection. By taking the characteristic vector field of this connection as a parallel vector field via the Levi-Civita connection, we examine some  curvature properties of Riemannian manifolds. We discuss Ricci-semi symmetry and we consider the conformal curvature tensor. Finally, we study hypersurfaces of Riemanninan manifolds admitting a type of semi-symmetric non-metric connection with a parallel  characteristic vector field. We take an example of a Riemannian manifold and we apply our results.