Journal of the
Korean Mathematical Society JKMS

Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent. Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq 5$ are locally classified. It is also proved that if $M$ is one of Sasakian, $\alpha $-Sasakian, Kenmotsu or $\beta $-Kenmotsu manifolds, which is generalized Ricci-recurrent with cyclic Ricci tensor and non-zero $A\left( \xi \right) $ everywhere; then $M$ is an Einstein manifold.

Keywords: Sasakian, $\alpha $-Sasakian, Kenmotsu, $\beta $-Kenmotsu, $f$-Kenmotsu, cosymplectic and trans-Sasakian structures, Ricci-recurrent, generalized Ricci-recurrent and Einstein manifolds.

MSC numbers: Primary 53C25