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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
##### Keywords:
CR manifold; CR-mapping; complete differential system
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