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.
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
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\by V.~K.~Beloshapka
\paper Representation of the Group of Holomorphic Symmetries of a Real Germ in the Symmetry Group of Its Model Surface
\jour Mat. Zametki
\yr 2007
\vol 82
\issue 4
\pages 515--518
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\jour Math. Notes
\yr 2007
\vol 82
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Linking options:
https://www.mathnet.ru/eng/mzm4019
https://doi.org/10.4213/mzm4019
https://www.mathnet.ru/eng/mzm/v82/i4/p515
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