η-Ricci solitons on Lorentzian β-Kenmotsu manifold

Abstract

휂-Ricci solitons on Lorentzian 훽-Kenmotsu manifold are considered an manifolds satisfying certain curvature Conditions, R(ξ,X).S=0, S(ξ,X).R=0, W2(ξ,X).S=0,S(ξ,X).W2=0 We proved that in Lorentzian β-Kenmotsu manifold (M,φ,ξ,η,푔). Then the existence of an 휂-Ricci solitons implies that M is Einstein manifold and if the Ricci curvature tensor satisfies, S(ξ,X).R=0, then Ricci solitons M is steady. If the condition 휇=0, then 휆=0, which shows that 휆is steady