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

Abstract

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 [Formula: see text] and [Formula: see text]. Initially, the tensor-based characterization of semisymmetric Lorentz para-Kenmotsu manifolds is studied. Subsequently, we consider the Lorentzian para-Kenmotsu manifold, which admits almost [Formula: see text]-Ricci solitons via these curvature tensors. According to the [Formula: see text] and [Formula: see text] curvature tensors, Ricci pseudosymmetry notions of Lorentzian para-Kenmotsu manifolds accepting [Formula: see text]-Ricci soliton have been developed. Following that, required conditions for the Lorentzian para-Kenmotsu manifold, admitting [Formula: see text]-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 [Formula: see text] and [Formula: see text] curvature tensors are investigated. We obtained the necessary and sufficient conditions for an invariant submanifold of a para-Kenmotsu to be [Formula: see text] and [Formula: see text] pseudoparallel.