η- ricci solitons defined with W8− curvature tensor and cyclic ricci tensor on para-kenmotsu manifolds

Abstract

In this Paper η- Ricci solitons are considered on Para- Kenmotsu manifolds satisfying (ξ,.)S.W8 = 0 and (ξ,.)W8.S = 0. The results of Blaga [1] for W2 have motivated us to use the same conditions on W8. We have proved that the Para- Kenmotsu manifolds satisfying (ξ,.)W8.S = 0. Are quasi- Einstein Manifolds and those satisfying (ξ,.)S.W8 = 0, are Einstein Manifolds. At the end of the paper it has been proven that the para- Kenmotsu manifolds with cyclic Ricci tensor and η− Ricci soliton structure are quasi-Einstein manifolds.