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## Annales Polonici Mathematici

1998 | 70 | 1 | 85-97
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
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
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
85-97
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-10-06
poprawiono
1998-05-22
Twórcy
autor
• Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia 5005
Bibliografia
• [Be] V. K. Beloshapka, On the dimension of the automorphism group of an analytic hypersurface, Izv. Akad. Nauk SSSR Ser. Mat. 93 (1979), 243-266 (in Russian).
• [CM] S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271.
• [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.
Typ dokumentu
Bibliografia
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