On some special classes of Kenmotsu manifolds

Abstract

We investigate the classes of Kenmotsu manifolds which satisfy the condition of being eta-Einstein, having eta-parallel Ricci tensor, R(xi, X) (.) Z = 0, R(xi, X) (.) R = 0, Z(xi, X) (.) Z = 0, Z(xi, X) (.) R = 0, Z(xi, X) (.) S = 0 or being Ricci-pseudosymmetric, where R, Z and S denote the curvature tensor, the concircular curvature tensor and the Ricci tensor, respectively. We also prove that a transformation in a Kenmotsu manifold under certain conditions is an isometry.