Transversal Lie group actions on abstract CR manifolds
It is shown that if an abstract CR manifold M has a local transversal Lie group action, then M is locally embeddable as a generic submanifold of \({\mathbb{C}}^ n\). Under the additional assumption that the infinitesimal action of the group forms a subbundle of TM, it is also shown that the action has a local holomorphic extension to \({\mathbb{C}}^ n\) in this embedding. Furthermore, it is shown that there is a unique embedding with this property, up to biholomorphism. Finally, if the action is strictly transversal to the CR structure, it is proved that any CR function can be locally decomposed as a finite sum of boundary values of holomorphic functions in open wedges with edge M.
generic submanifold of \({\mathbb{C}}(\sup \) n)
scientific article; zbMATH DE number 4101589