On three-dimensional conformally flat quasi-Sasakian manifolds (Q1375688)

With the aid of the structure function \(\beta\) of a 3-dimensional quasi-Sasakian manifold \(M\), necessary and sufficient conditions are given for \(M\) to be conformally flat. It is proved that if \(M\) is conformally flat and \(\beta=\text{ const.}\), then (a) \(M\) is locally a product of \(\mathbb{R}\) and a 2-dimensional Kähler-space of constant Gauss curvature, or (b) \(M\) is of constant positive curvature. An example is also given.