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Complete differential system for the mappings of CR manifolds of nondegenerate Levi forms. (English) Zbl 0892.32015
Let \(M\) be a \(C^\omega\) CR manifold of dimension \(2m+1\) with nondegenerate Levi-form and let \(N\) be a \(C^\omega\) real hypersurface in \(C^{n+1}\) with \(n \geq m\). Let \(f:M \to N\) be a CR-mapping.
By using the notion of the complete differential system for a CR-mapping, the author gives a sufficient condition for \(f\) to be real analytic. As a corollary the author proves that if \(N\) is a \(C^\omega\) CR manifold with non-degenerate Levi form and \(\varphi\) is a CR-automorphism of \(N\), then \(\varphi\) is determined by its second jet at a point.

MSC:
32V05 CR structures, CR operators, and generalizations
32V99 CR manifolds
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