On Kenmotsu manifolds satisfying certain curvature conditions

Abstract

The object of the present paper is to study some curvature conditions on Kenmotsu manifolds. Also, we classify Kenmotsu manifolds which satisfy $P\cdot \tilde{C}=0,\tilde{C}\cdot \tilde{C}=0,\tilde{Z}\cdot \tilde{C}=0,\tilde{C}\cdot \tilde{Z}=0$ and $C\cdot \tilde{C}=0$, where $P$ is the projective curvature tensor, $\tilde{Z}$ is the concircular curvature tensor, $\tilde{C}$ is the quasi-conformal curvature tensor and $C$ is the conformal curvature tensor.