Some Solitons on Lorentzian Para-Kenmotsu Manifolds - Mandal, Abhijit; Mallik, Meghlal (Sarajevo Journal of Mathematics, 2025)
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 contains an 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 .) _W_2 .S=0 and ( ξ .) _S.W_2=0, where R, S and W_2 are, respectively, the Riemannian curvature tensor, Ricci curvature tensor and W_2-curvature tensor.