The main object of this work is to study the generalized
B-curvature tensor in an
n-dimensional Lorentzian para-Kenmotsu (briefly,
) manifold along a semi-symmetric metric connection
. First, in an
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The main object of this work is to study the generalized
B-curvature tensor in an
n-dimensional Lorentzian para-Kenmotsu (briefly,
) manifold along a semi-symmetric metric connection
. First, in an
-manifold, we explore certain flatness conditions, namely,
,
,
, and
conditions, which all result in an
-Einstein manifold. Furthermore, in an
-manifold, we study the curvature conditions
and
= 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.
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