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On generalized Ricci-recurrent trans-Sasakian manifolds

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Abstract

Generalized Ricci-recurrent trans-Sasakian manifolds are studied.Among others, it is proved that a generalized Ricci-recurrentcosymplectic manifold is always recurrent. GeneralizedRicci-recurrent trans-Sasakian manifolds of dimension geq 5 arelocally classified. It is also provedthat if M is one of Sasakian, alpha -Sasakian, Kenmotsu or beta %-Kenallowbreak motsu manifolds, which is generalized Ricci-recurrent withcyclic Ricci tensor and non-zero Aleft( xi right) everywhere; then Mis an Einstein manifold.

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