Characterization of almost -curvature tensor on Riemannian manifold

Abstract

In this paper we introduce a new tensor named almost -curvature tensor , which generalizes the projective curvature tensor and -curvature tensor. First we deduce some basic geometric properties of . Then, we study pseudo -symmetric manifolds , . We provide several interesting results. Among others we prove that in a if the associated vector field is a unit parallel vector field, then the manifold reduces to a pseudo symmetric manifold. Finally, we construct a non-trivial Lorentzian metric of .