Abstract
The main result of this paper gives a characterization of left-invariant almost [Formula: see text]-coKähler structures on three-dimensional (3D) semidirect product Lie groups [Formula: see text] in terms of the matrix [Formula: see text]. Then, we study the harmonicity of the Reeb vector field [Formula: see text] of a simply connected homogeneous almost [Formula: see text]-coKähler three-manifold, in terms of the Gaussian curvature of the canonical foliation.
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