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On the Schwarz symmetry principle in a model case. (English) Zbl 0919.32011

Let \(f:M\rightarrow M'\) be a \(C^{\infty}\)-smooth CR diffeomorphism between real analytic, holomorphically non degenerate hypersurfaces in \(\mathbb{C^n}\), which is holomorphic on one side of \(M\). The authors establish the Schwarz symmetry principle in case \(M'\) is in addition rigid and polynomial. It is not required that \(M\) be algebraic.

MSC:

32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
32C05 Real-analytic manifolds, real-analytic spaces
32V99 CR manifolds
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