An Analysis of Generalized N-Projective Curvature Tensor of Lorentzian β-Kenmotsu Manifolds Admitting Zamkovoy Connection

Abstract

This paper investigates Lorentzian β-Kenmotsu Manifolds with Zamkovoy connections. We introduce a new (0, 2) type symmetric tensor Z˚, derived from the N-projective curvature tensor, termed the generalized N-projective curvature tensor. We prove that when these manifolds exhibit generalized N-projectively semi-symmetric properties, they become Einstein manifolds. Additionally, we show that the condition of generalized N-projective ϕ-symmetry on Lorentzian β-Kenmotsu Manifold with Zamkovoy connection implies that the manifold is again an Einstein manifold.