Conformally flat almost cosymplectic 3-manifolds

AbstractIn this paper, we consider an almost cosymplectic 3-manifold M such that its scalar curvature is invariant along the Reeb vector field. We prove that if the Reeb vector field of M is harmonic, then M is conformally flat if and only if it is locally isometric to the product ℝ × N2(c), where N2(c) is a Kähler surface of constant sectional curvature c. Almost cosymplectic 3-manifolds on which the Reeb vector field satisfies the h-a condition together with conformal flatness are also classified.