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Transversal Lie group actions on abstract CR manifolds. (English) Zbl 0673.32021
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.
Reviewer: M.S.Baouendi

MSC:
32V40 Real submanifolds in complex manifolds
32M05 Complex Lie groups, group actions on complex spaces
57S20 Noncompact Lie groups of transformations
57S15 Compact Lie groups of differentiable transformations
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References:
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