Local criteria for non embeddability of Levi-flat manifolds

TL;DR

This paper establishes local criteria to determine when Levi-flat manifolds cannot be smoothly embedded, using an analogue of Ueda theory to analyze neighborhood structures of hypersurfaces with trivial normal bundles.

Contribution

It introduces a novel local criterion for non-embeddability of Levi-flat manifolds based on an adapted Ueda theory framework.

Findings

Provides conditions for non-embeddability of Levi-flat manifolds.

Develops an analogue of Ueda theory for hypersurfaces with trivial normal bundles.

Offers tools for analyzing neighborhood structures in complex manifolds.

Abstract

We give local criteria for smooth non-embeddablity of Levi-flat manifolds. For this purpose, we pose an analogue of Ueda theory on the neighborhood structure of hypersurfaces in complex manifolds with topologically trivial normal bundles.