CR embeddings of CR manifolds

TL;DR

This paper weakens the conditions needed for CR manifolds to admit local embeddings, replacing the requirement of a finite dimensional solvable transverse Lie algebra with a less restrictive finite dimensional extension.

Contribution

It introduces a new, weaker sufficient condition for CR manifolds to admit local CR embeddings, broadening the class of manifolds that can be embedded.

Findings

Weaker sufficient condition for CR embedding.

Extension condition replaces solvable Lie algebra requirement.

Broader applicability of CR embedding criteria.

Abstract

We improve results of Baouendi, Rothschild and Treves and of Hill and Nacinovich by finding a much weaker sufficient condition for a CR manifold of type $(n,k)$ to admit a local CR embedding into a CR manifold of type $(n+\ell,k-\ell)$. While their results require the existence of a finite dimensional solvable transverse Lie algebra of vector fields; we require only a finite dimensional extension.