SOME TYPES OF η-RICCI SOLITONS ON LORENTZIAN PARA-SASAKIAN MANIFOLDS

Abstract

In this paper we study some types of  η-Ricci solitons on Lorentzianpara-Sasakian manifolds and we give an example of  η-Ricci solitons on 3-dimensional Lorentzian para-Sasakian manifold. We obtain the conditions of  η-Ricci soliton on ϕ-conformally flat, ϕ-conharmonically flat and ϕ-projectivelyflat Lorentzian para-Sasakian manifolds, the existence of η-Ricci solitons implies that (M,g) is  η-Einstein manifold. In these cases there is no Ricci solitonon M with the potential vector field