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On generalized Ricci-recurrent trans-Sasakian manifolds. (English) Zbl 1025.53023

A Riemannian manifold \((M,g)\) is called generalized Ricci-recurrent if there exist \(1\)-forms \(A\) and \(B\) such that its Ricci tensor satisfies \(\nabla_X \text{Ric}(Y,Z)= A(X) \text{Ric}(Y,Z)+B(X)g(Y,Z)\). The authors study generalized Ricci-recurrent manifolds which are in addition trans-Sasakian, and give a local classification of these in dimensions \(n\geq 5\). If Ric is, in addition, cyclic, and \(A\) is never zero, the manifold is necessarily Einstein.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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