Abstract. Let (Mⁿ, g) (n ≥ 3) be a Riemannian manifold with metric g. If its projective Ricci tensor P satisfies the condition (∇_xP)(Y,Z) = 2A(X)P(Y,Z) + A(Y)P(X,Z) + A(Z)P(Y,X), where A is a nonzero 1-form, g(X,ρ) = A(X) for every vector field X and ∇ denotes the operator of covariant differentiation with respect to g, then the manifold will be called a Pseudo-Projective Ricci symmetric manifold and such an n-dimensional manifold will be denoted by (PWRS)_n. In this paper it is shown that the scalar curvature of a (PWRS)_n is a nonzero constant and its Ricci curvature in the direction of ρ is r/n. Further, several properties of such a manifold are established.

Full-text: PDF