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

On Pseudo-Projective Ricci Symmetric Manifolds

M.C. Chaki, S.K. Saha
Department of Pure Mathematics, Calcutta University, Calcutta
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.

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