Ricci solitons on almost Kenmotsu 3-manifolds

Source abstract

Abstract Let ( M 3 , g ) be an almost Kenmotsu 3-manifold such that the Reeb vector field is an eigenvector field of the Ricci operator. In this paper, we prove that if g represents a Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M 3 is locally isometric to either the hyperbolic space ℍ 3 (−1) or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure. In particular, when g represents a gradient Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M 3 is locally isometric to either ℍ 3 (−1) or ℍ 2 (−4) × ℝ.