η - Ricci solitons on Lorentzian Para- Sasakian manifolds L. F. UWIMBABAZI Ruganzu 1 , S.K. Moindi 2 , G.P. Pokhariyal 3 J.Katende 4 School of Mathematics, University of Nairobi, P.O. Box 30197-00100, Nairobi, Kenya ruganzu01@gmail.com 1 Abstract In the present Paper η- Ricci solitons on Lorentzian Para- Sasakian manifolds satisfying (ξ,.)s.W8 = 0 and (ξ,.)W 8 .S = 0 are discussed. 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.W8 = 0 and having η- Ricci soliton structureL ξ g +2s +2λg +2μη ⊗ η are quasi-Einstein manifolds and those satisfying (ξ,.)W 8 .S = 0 are Einstein manifolds. Keywords and phrases. Ricci solitons, η−Ricci solitons, Lorentzian Para-Sasakian manifolds, W 8 curvature tensor. 2010 Mathematics subject classification. 53C15, 53C25, 53C44. 1 Introduction In last two decades the Ricci solitons have interested most of differential geometers as topic of study on different manifolds. Contact and para-Contact have been among the most considered in the study of those solutions of Ricci flows. The interest in study has considerably increased due to the recent Perelman proof of Poincar´ e Conjecture using Ricci flows. Ricci Flows have been introduced by Hamilton[1]in 1982 as gen- eralization of Einstein metrics. The Ricci flow is an evolution equation of heat equation type for the metric on Reimannian manifold and is defined as ∂ ∂t g ij (t)= −2S ij , (1.1) 1 International Journal of Trend in Research and Development, Volume 5(3), ISSN: 2394-9333 www.ijtrd.com IJTRD | May-Jun 2018 Available Online@www.ijtrd.com 539