Generalized B-Curvature Tensor in Lorentzian Para-Kenmotsu Manifold with Semi-Symmetric Metric Connection

The main object of this work is to study the generalized B-curvature tensor in an n-dimensional Lorentzian para-Kenmotsu (briefly, (LPK)n) manifold along a semi-symmetric metric connection ∇¯. First, in an (LPK)n-manifold, we explore certain flatness conditions, namely, B¯(Y,Z)X=0, B¯(Y,Z)ζ=0, g(B¯(φY,φZ)φX,φW)=0, and B¯(Y,Z)·φ=0 conditions, which all result in an η-Einstein manifold. Furthermore, in an (LPK)n-manifold, we study the curvature conditions B¯.Q=0 and B¯.Q¯ = 0, which provide the scalar curvature. The generalized B-curvature tensor blends the features of different curvature tensors, allowing researchers to study conditions like semi-symmetry, pseudo-symmetry in a unified framework. Conditions like B-semi-symmetry correspond to conservation laws or stability properties in physical systems.