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

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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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     author = {V. K. Beloshapka},
     title = {Representation of the {Group} of {Holomorphic} {Symmetries} of a {Real} {Germ} in the {Symmetry} {Group} of {Its} {Model} {Surface}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {515--518},
     publisher = {mathdoc},
     volume = {82},
     number = {4},
     year = {2007},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a4/}
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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/