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 Mat. Zametki, 2007, Volume 82, Issue 4, Pages 515–518 (Mi mz4019)

Representation of the Group of Holomorphic Symmetries of a Real Germ in the Symmetry Group of Its Model Surface

V. K. Beloshapka

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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, tangent model surface, Lie group

DOI: https://doi.org/10.4213/mzm4019

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English version:
Mathematical Notes, 2007, 82:4, 461–463

Bibliographic databases:

UDC: 517.53
Revised: 15.03.2007

Citation: V. K. Beloshapka, “Representation of the Group of Holomorphic Symmetries of a Real Germ in the Symmetry Group of Its Model Surface”, Mat. Zametki, 82:4 (2007), 515–518; Math. Notes, 82:4 (2007), 461–463

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz4019
• https://doi.org/10.4213/mzm4019
• http://mi.mathnet.ru/eng/mz/v82/i4/p515

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. J. Merker, M. Sabzevari, “The Cartan equivalence problem for Levi-non-degenerate real hypersurfaces $M^3\subset\mathbb C^2$”, Izv. Math., 78:6 (2014), 1158–1194
2. Beloshapka V.K. Kossovskii I.G., “the Sphere in C-2 as a Model Surface For Degenerate Hypersurfaces in C-3”, Russ. J. Math. Phys., 22:4 (2015), 437–443
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