Geometry of Kenmotsu manifolds admitting Z-tensor

Abstract

The object of this paper is to study Kenmotsu manifolds admitting Z−tensor, which is a generalization of Einstein tensor that comes from general relativity. We define a special type of quarter-symmetric non-metric ϕ and η-connection on a Kenmotsu manifold and we examine some geometric properties of such manifolds with Z−tensor. Some semi-symmetry conditions related to Z−tensor are studied on Kenmotsu manifolds and finally, we observe our results on a 5-dimensional Kenmotsu manifold.