Some curvature characterizations on Kenmotsu metric spaces

Abstract

The purpose of this study is to characterize Kenmotsu manifolds that satisfy specific curvature conditions. We give the Kenmotsu manifold curvature tensors satisfying the conditions RW₅ = 0, RW₇ = 0, RW₉ = 0 and φ-RW₀* = 0. Also we consider a W₀*-flat and a φ-W₀*-flat Kenmotsu metric manifolds. As a result, M is an η-Einstein Kenmotsu metric manifold.