Abstract

In the present paper we study 3-dimensional contact metric manifolds with φQ = Qφ admitting generalized Ricci solitons and generalized gradient Ricci solitons. It is proven that if a 3-dimensional contact metric manifold satisfying φQ = Qφ admits a generalized Ricci soliton with non zero soliton vector eld V being pointwise collinear with the characteristic vector field ξ, then the manifold is Sasakian. Also it is shown that if a 3-dimensional compact contact metric manifold with φQ = Qφ admits a generalized gradient Ricci soliton then either the soliton is trivial or the manifold is at or the scalar curvature is constant.