Non-embeddability of certain classes of Levi flat manifolds
Giuseppe Della Sala
TL;DR
This paper proves that certain Levi flat manifolds with specific boundary and foliation properties cannot be embedded as CR hypersurfaces in complex manifolds, based on a result by Barrett.
Contribution
It establishes non-embeddability for classes of Levi flat manifolds with boundary and particular holonomy conditions, extending Barrett's result.
Findings
Certain Levi flat manifolds cannot be CR embedded in complex manifolds.
Non-embeddability depends on the presence of a compact leaf with flat, contracting holonomy.
The result applies to specific classes of Levi flat manifolds with boundary.
Abstract
On the basis of a result of Barrett, 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 embedding as a hypersurface of a complex manifold.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory