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Proceedings of the American Mathematical Society

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On the realizability of Lewy structures

Author: Abdelhamid Meziani
Journal: Proc. Amer. Math. Soc. 124 (1996), 2767-2772
MSC (1991): Primary 32F25; Secondary 53C40
MathSciNet review: 1350956
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Abstract: We prove that a nondegenerate CR structure with signature
$(p,n-p)$ at $0\in \mathbb {R}^{2n+1}$ and with $n$ first integrals $z_{1},\cdots ,z_{n}$ satisfying

\begin{equation*}dz_{1}\wedge d\bar {z}_{1}\wedge \cdots \wedge dz_{n}\wedge d\bar {z}_{n} \ne 0\end{equation*}

is realizable if and only if an action of the group $O(2p,2n-2p)$ leaves invariant a one-dimensional subbundle of the structure bundle.

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Additional Information

Abdelhamid Meziani
Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199

Received by editor(s): December 8, 1994
Received by editor(s) in revised form: March 10, 1995
Communicated by: Eric Bedford
Article copyright: © Copyright 1996 American Mathematical Society