Non-embeddability of certain classes of Levi flat manifolds

Abstract

On the basis of a result of Barrett [2], we show that members of certain classes of abstract Levi flat manifolds with boundary, whose Levi foliation contains a compact leaf with contracting, flat holonomy, admit no $\mathit{CR}$ embedding as a hypersurface of a complex manifold. In particular, it follows that the foliation constructed in [6] is not embeddable.