Almost η-Ricci Solitons on the Pseudosymmetric Lorentzian Para-Kenmotsu Manifolds

Abstract

In this paper, we consider Lorentzian para-Kenmotsu manifold admitting almost $\eta-$Ricci solitons by virtue of some curvature tensors. Ricci pseudosymmetry concepts of Lorentzian para-Kenmotsu manifolds admitting $\eta-$Ricci soliton have introduced according to the choice of some curvature tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ After then, according to the choice of the curvature tensors, necessary conditions are given for Lorentzian para-Kenmotsu manifold admitting $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are given and classifications have made under the some conditions.