Ricci Solitons on Almost Co-Kähler Manifolds

In this paper, we prove that if an almost co-Kähler manifold of dimension greater than three satisfying [STIX]x1D702 -Einstein condition with constant coefficients is a Ricci soliton with potential vector field being of constant length, then either the manifold is Einstein or the Reeb vector field is parallel. Let M be a non-co-Kähler almost co-Kähler 3-manifold such that the Reeb vector field [STIX]x1D709 is an eigenvector field of the Ricci operator. If M is a Ricci soliton with transversal potential vector field, then it is locally isometric to Lie group $E(1,1)$ of rigid motions of the Minkowski 2-space.