Geodesic
Representation of the Group of Holomorphic Symmetries of a Real Germ in the Symmetry Group of Its Model Surface
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 515-518 Cet article a éte moissonné depuis la source Math-Net.Ru

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Local polynomial models of real submanifolds of complex space were constructed and studied in a series of papers. Among the main features of model surfaces, there is the property that the dimension of the local group of holomorphic symmetries of a germ does not exceed that of the same group of the tangent model surface of this germ. In the paper, this assertion is rendered much stronger; namely, it is proved that the connected component of the identity element in the symmetry group of a nondegenerate germ is isomorphic as a Lie group to a subgroup of the symmetry group of its tangent model surface.
Keywords: germ, holomorphic symmetry group
Mots-clés : tangent model surface, Lie group. 
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V. K. Beloshapka. Representation of the Group of Holomorphic Symmetries of a Real Germ in the Symmetry Group of Its Model Surface. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 515-518. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a4/

[1] V. K. Beloshapka, “Veschestvennye podmnogoobraziya kompleksnogo prostranstva ikh polinomialnye modeli, avtomorfizmy i problemy klassifikatsii”, UMN, 57:1 (2002), 3–44 | MR | Zbl

[2] V. K. Beloshapka, “Universalnaya model veschestvennogo podmnogoobraziya”, Matem. zametki, 75:4 (2004), 507–522 | MR | Zbl

[3] M. S. Baouendi, L. P. Rothschild, J. Winkelmann, D. Zaitsev, “Lie group structures of diffeomorphisms and applications to CR manifolds”, Ann. Inst. Fourier (Grenoble), 54 (2004), 1279–1303 | MR | Zbl

[4] A. G. Vitushkin, “Golomorfnye otobrazheniya i geometriya poverkhnostei”, Sovremennye problemy matematiki. Fundamentalnye napravleniya, 7, VINITI, M., 1985, 167–226 | MR | Zbl

[5] R. V. Gammel, I. G. Kossovskii, “Obolochka golomorfnosti modelnoi poverkhnosti stepeni tri i fenomen “zhestkosti” ”, Kompleksnyi analiz i prilozheniya: Sbornik statei, Tr. MIAN, 253, 2006, 30–45 | MR