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On pseudo Ricci symmetric manifolds. (English) Zbl 0689.53011
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