Triviality of scalar linear type isotropy subgroup by passing to an alternative canonical form of a hypersurface

• Autorzy: Vladimir V. Ežov
• Języki publikacji: EN

Abstrakty

EN

The Chern-Moser (CM) normal form of a real hypersurface in $ℂ^N$ can be obtained by considering automorphisms whose derivative acts as the identity on the complex tangent space. However, the CM normal form is also invariant under a larger group (pseudo-unitary linear transformations) and it is this property that makes the CM normal form special. Without this additional restriction, various types of normal forms occur. One of them helps to give a simple proof of a (previously complicated) theorem about triviality of the scalar linear type isotropy subgroup of a nonquadratic hypersurface. An example of an analogous nontrivial subgroup for a 2-codimensional CR surface in $ℂ^4$ is constructed. We also consider the question whether the group structure that is induced on the family of normalisations to the CM normal form via the parametrisation of the isotropy automorphism group of the underlining hyperquadric coincides with the natural composition operation on the biholomorphisms.

Słowa kluczowe

EN

CR automorphisms; canonical form; scalar linear type isotropy

Kategorie tematyczne

• 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
• 32C05: Real-analytic manifolds, real-analytic spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 70
• Numer: 1
• Strony: 85-97

Daty

wydano

1998

otrzymano

1997-10-06

poprawiono

1998-05-22

Twórcy

autor

Vladimir V. Ežov

• Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia 5005

Bibliografia

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• [ES] V. V. Ežov and G. Schmalz, Holomorphic automorphisms of quadrics, Math. Z. 216 (1994), 453-470.
• [Lo1] A. V. Loboda, On local automorphisms of real-analytic hypersurfaces, Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981), 620-645 (in Russian).
• [Lo2] A. V. Loboda, Generic real-analytic manifolds of codimension 2 in $ℂ^4$ and their biholomorphic mappings, Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), 970-990 (in Russian).
• [Sch] G. Schmalz, Über die Automorphismen einer streng pseudokonvexen CR-Mannigfaltigkeit der Kodimension 2 im $ℂ^4$, Math. Nachr., to appear.