On conformally flat pseudo-Ricci symmetric manifolds

On generalized Pseudo Ricci symmetric manifolds

“…which reduces to a pseudo Ricci symmetric manifold introduced and studied by one of the authors (Chaki) [2]. This justifies the name generalized Pseudo Ricci symmetric manifold for the manifold defined by (9) and the symbol G(PRS)n for it.…”

“…The notions of Pseudo symmetric and Pseudo Ricci symmetric manifolds were introduced by one of the authors (Chaki) in 1987 [1] and 1988 [2] respectively.…”

On weakly cyclic Z symmetric spacetimes

“…If ϕ = 0, we recover from (1.4) a (W RS) n , and as a particular case pseudo Ricci symmetric manifolds (P RS) n [4]. If ϕ = − r n (classical Z tensor) and A is replaced by 2A and B and D are replaced by A, then…”

“…It is a generalization of the weakly Ricci symmetric manifolds [4], and pseudo Ricci symmetric manifolds [4] and pseudo projective Ricci symmetric manifolds [7]. A non-flat Riemannian or a semi-Riemannian manifold (M n , g)(n > 2) is called weakly cyclic Z symmetric [11] and denoted by (W CZS) n , if the generalized Z tensor is non-zero and satisfies the condition…”

On pseudo symmetric and pseudo Ricci symmetricK-contact manifolds

“…for every vector field X and V denotes the operator of covariant differentation with respect to the metric g. Such a manifold was called a pseudo symmetric manifold, A was called its associated 1-form and an n-dimensional manifold of this kind was denoted by (PS)n-In a subsequent paper ( [3]) M.C. Chaki introduced another type of non-flat Riemannian manifolds (M n, g) (n >_ 3) whose Ricci tensor S type (0, 2) satisfies the condition…”