CR embeddings of CR manifolds

Abstract

<p>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 (<i>n, k</i>) to admit a local CR embedding into a CR manifold of type (<i>n+ℓ,k−ℓ</i>) . While their results require the existence of a finite dimensional solvable transverse Lie algebra of vector fields, we require only a finite dimensional extension.</p>