Ricci Solitons on Almost Co-Kähler Manifolds

Abstract In this paper, we prove that if an almost co-Kähler manifold of dimension greater than three satisfying 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 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.