On pseudo Ricci symmetric manifolds. (English) Zbl 0689.53011

Chaki, M. C.

Bulg. J. Phys. 15, No. 6, 526-531 (1988).

By an n-dimensional pseudo-Ricci symmetric manifold, the author understands a Riemannian manifold \((M^ n,g)\) whose Ricci tensor S satisfies the condition \[ V_ XS(Y,Z)=2A(X)S(Y,Z)+A(Y)S(Z,X)+A(Z)S(X,Y), \] where \(\nabla\) is the Levi- Civita connection of g and A is a non-zero 1-form on \(M^ n\). The existence and several properties of such a manifold are established in this work.

Reviewer: V.Cruceanu

MSC:

53B20

Local Riemannian geometry

Keywords:

pseudo-Ricci symmetric manifold