Compact three-dimensional manifolds with commutative fundamental group embedded into \(\mathbb{C}\mathbb{P}^ 2\) (Q1897215)

The author continues his study concerning the Levi form of a compact three-dimensional real analytic manifold [Math. Notes 54, No. 4, 1035-1044 (1993); translation from Mat. Zametki 54, No. 4, 82-97 (1993; Zbl 0809.32007)]. If a three-dimensional manifold is embedded into \(\mathbb{C} \mathbb{P}^2\) with an identically zero Levi form then \(M\) is orientable and there arises an orientable analytic foliation \(\{L_\alpha\}\) of codimension 1 on \(M\), the leaves of which are complex submanifolds of \(\mathbb{C} \mathbb{P}^2\) and are all noncompact. The author proves that a three-dimensional compact manifold \(M\) with commutative fundamental group cannot be embedded into \(\mathbb{C} \mathbb{P}^2\) so that its Levi form identically vanishes.