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η-Ricci solitons on Lorentzian para-Sasakian manifolds

Blaga Adara M. (West University of Timişoara, Department of Mathematics, Timişoara, Romnia)

We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds satisfying certain curvature conditions: R(ξ,X)•S = 0 and S•R(ξ,X)=0. We prove that on a Lorentzian para-Sasakian manifold (M,φ,ξ,η,g), if the Ricci curvature satisfies one of the previous conditions, the existence of η-Ricci solitons implies that (M,g) is Einstein manifold. We also conclude that in these cases there is no Ricci soliton on M with the potential vector field ξ. On the other way, if M is of constant curvature, then (M,g) is elliptic manifold. Cases when the Ricci tensor satisfies different other conditions are also discussed.

Keywords: η-Ricci solitons, Lorentzian para-Sasakian structure