#### Bulg. J. Phys. vol.21 no.1-2 (1994), pp. 001-007

#### On Pseudo-Projective Ricci Symmetric Manifolds

M.C. Chaki

go back^{}, S.K. Saha^{}*Department of Pure Mathematics, Calcutta University, Calcutta*Abstract.Let (M) (^{n}, gn≥ 3) be a Riemannian manifold with metricg. If its projective Ricci tensorPsatisfies the condition (∇_{x}P)(Y,Z) = 2A(X)P(Y,Z) +A(Y)P(X,Z) +A(Z)P(Y,X), whereAis a nonzero 1-form,g(X,ρ) =A(X) for every vector fieldXand ∇ denotes the operator of covariant differentiation with respect tog, then the manifold will be called a Pseudo-Projective Ricci symmetric manifold and such ann-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 ofρisr/n. Further, several properties of such a manifold are established.