Classification of homogeneous almost cosymplectic three-manifolds

The purpose of this paper is to classify all simply connected homogeneous almost cosymplectic three-manifolds. We show that each such three-manifold is either a Lie group G equipped with a left invariant almost cosymplectic structure or a Riemannian product of type R x N, where N is a Kahler surface of constant curvature. Moreover, we find that the Reeb vector field of any homogeneous almost cosymplectic three-manifold, except one case, defines a harmonic map. (C) 2011 Elsevier B.V. All rights reserved.