M - projective curvature tensor equipped with an ϵ-kenmotsu manifold

In this paper, we studied the properties of ϵ-Kenmotsu manifolds that posses an M -projective curvature tensor. We have shown that ϵ-Kenmotsu manifolds with an M -projectively flat and irrotational M -projective curvature tensor are locally isometric to the hyperbolic space Hn(c), where c = −ϵ2. Additionally, we have investigate the condition R(X, Y ) · S = 0 for M -projectively flat ϵ-Kenmotsu manifolds. Then we focused on the analysis of ϵ-Kenmotsu manifolds with a conservative M -projective curvature tensor. Lastly, we have certain geometric results for ϵ-Kenmotsu manifolds that satisfy the relation M (X, Y ) · R = 0.