On a criterion for local embeddability of 3-dimensional CR-structures

TL;DR

This paper introduces quasi-Fefferman metrics, a CR-invariant class of Lorentzian metrics, and establishes a Ricci curvature criterion for the local embeddability of 3-dimensional CR-structures, extending previous results.

Contribution

It generalizes the Fefferman metric to better control Ricci curvature and provides a new criterion for CR-structure embeddability based on this class.

Findings

Defined quasi-Fefferman metrics as a CR-invariant class.

Established a Ricci curvature criterion for embeddability.

Extended previous results by Hill et al.

Abstract

We introduce a CR-invariant class of Lorentzian metrics on a circle bundle over a 3-dimensional CR-structure, which we call quasi-Fefferman metrics. These metrics generalise the Fefferman metric but allow for more control of the Ricci curvature. Our main result is a criterion for embaddability of 3-dimensional CR-structures in terms of the Ricci curvature of the quasi-Fefferman metrics in the spirit of the results by Hill et al.