On M-projective curvature tensor of Lorentzian β-Kenmotsu manifold

Abstract

In this paper, we explore the characteristics of Lorentzian β - Kenmotsu manifolds admitting M - projective curvature tensor. We demonstrate that M - projectively flat and irrotational M - projective curvature tensor of Lorentzian β - Kenmotsu manifolds are locally isometric to hyperbolic space Hⁿ(c), where c = −β². Further, we deal with the M - projectively flat Lorentzian β - Kenmotsu manifold that satisfies the condition R(X, Y )・S = 0. The Lorentzian β - Kenmostu manifold with conservative M - projective curvature tensor is the subject of our next analysis. Finally, we obtain certain geometrical facts if the Lorentzian β - Kenmotsu manifold satisfies the relation M(X, Y )・R = 0.