Three dimensional contact metric manifolds with Cotton solitons (Q2073417)

Three-dimensional contact metric manifolds admitting Cotton solitons are considered. Under some special conditions, classifications of three-dimensional contact metric manifolds admitting gradient Cotton solitons and Cotton solitons with potential vector field are obtained. Also under certain conditions, classifications of some types of three-dimensional so-called \((\kappa,\mu,\nu)\)-contact metric manifolds admitting Cotton solitons are presented. In particular, it is proved that if a three-dimensional \((\kappa,\mu,\nu)\)-contact metric manifold admits a Cotton soliton such that the potential vector field \(V\) is the Reeb vector field \(\xi\), then this manifold is Sasakian.