Some Solitons on Lorentzian Para-Kenmotsu Manifolds

In this paper we study the nature of the Einstein soliton and η-Einstein soliton in the framework of Lorentzian para-Kenmotsu manifolds (briefly, LP-Kenmotsu manifolds). We find an expression for scalar curvature of LP-Kenmotsu manifolds admitting the Einstein soliton and η-Einstein soliton in various cases. We prove that if an LP-Kenmotsu manifold containsan η-Einstein soliton with a parallel Reeb vector field then the manifold is η-Einstein. We study the nature of the η-Einstein soliton on these manifolds with conformal, collinear and torse forming potential vector fields. We also study the η-Einstein soliton on these manifolds satisfying the curvature conditions: ( ξ .) R.S=0, ( ξ .) _W₂.S=0 and ( ξ .) S.W₂=0, where $R,$ S and W₂ are, respectively, the Riemannian curvature tensor, Ricci curvature tensor and W₂-curvature tensor.