On some important characterizations of Lorentz para-Kenmotsu manifolds on some special curvature tensors

In this paper, some properties of Lorentz para-Kenmotsu manifolds are studied using specified curvature tensors. The Lorentz para-Kenmotsu manifold is investigated in terms of the curvature tensors W-8 and W-9. Initially, the tensor-based characterization of semisymmetric Lorentz para-Kenmotsu manifolds is studied. Subsequently, we consider the Lorentzian para-Kenmotsu manifold, which admits almost eta-Ricci solitons via these curvature tensors. According to the W-8 and W-9 curvature tensors, Ricci pseudosymmetry notions of Lorentzian para-Kenmotsu manifolds accepting eta-Ricci soliton have been developed. Following that, required conditions for the Lorentzian para-Kenmotsu manifold, admitting eta-Ricci soliton to be Ricci semisymmetric, are presented based on the curvature tensors chosen. Further, various characterizations are provided, and classifications are made under certain conditions. Finally, the characterizations of the invariant submanifolds of Lorentz para-Kenmotsu manifold on the W(8 )and W-9 curvature tensors are investigated. We obtained the necessary and sufficient conditions for an invariant submanifold of a para-Kenmotsu to be W-8 and W-9 pseudoparallel.