η- Ricci solitons on lorentzian para- sasakian manifolds defined with W2−curvaturetensor

Abstract

In the present paper η- Ricci solitons on Lorentzian Para- Sasakian manifolds satisfying (ξ,.)s.W2 = 0 and (ξ,.)W2.S = 0 are treated. The results obtained on η- Ricci solitons on para- Kenmotsu manifolds have motivated us to investigate η- Ricci solitons on Lorentzian Para-Sasakian Manifolds satisfying the same conditions and quasi-similar results have been obtained. In fact, we have proved that Lorentzian Para- Sasakian manifolds satisfying (ξ,.) s.W2 = 0 and having η− Ricci soliton structure are Einstein or quasi-Einstein manifolds according to the value µ and λ. The same results have been proved on Manifolds satisfying (ξ,.)W2.S = 0.