CR embeddings of CR manifolds

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.