Lorentzian $CR$ structures and nonembeddability

TL;DR

This paper constructs Lorentzian CR hypersurface examples demonstrating that local embeddability can fail at isolated points despite being embeddable elsewhere, highlighting limitations of CR embedding theory.

Contribution

It introduces specific CR deformations of Lorentzian hypersurfaces showing nonembeddability at isolated points, advancing understanding of CR structure limitations.

Findings

CR deformations with isolated nonembeddability

Examples of Lorentzian hypersurfaces with partial embeddability

Insights into the local-global embeddability relationship

Abstract

In this paper we construct examples of $CR$ deformations of Lorentzian hypersurfaces which are $CR$ embeddable at all points outside an arbitrarily small compact set whose interior contains a point where $CR$ embeddablity is not possible.