Ricci tensors on three-dimensional almost coKähler manifolds

Abstract

Let M³ be a three-dimensional almost coKähler manifold such that the Ricci curvature of the Reeb vector field is invariant along the Reeb vector field. In this paper, we obtain some classification results of M³ for which the Ricci tensor is η-parallel or the Riemannian curvature tensor is harmonic.