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@article{1173629, author = {Ezhov, Vladimir and Kolář, Martin and Schmalz, Gerd}, article_number = {1}, keywords = {Normal form real hypersurface symmetry algebra}, language = {eng}, issn = {0022-2518}, journal = {INDIANA UNIVERSITY MATHEMATICS JOURNAL}, title = {Normal Forms and Symmetries of Real Hypersurfaces of Finite Type in C-2}, volume = {62}, year = {2013} }
TY - JOUR ID - 1173629 AU - Ezhov, Vladimir - Kolář, Martin - Schmalz, Gerd PY - 2013 TI - Normal Forms and Symmetries of Real Hypersurfaces of Finite Type in C-2 JF - INDIANA UNIVERSITY MATHEMATICS JOURNAL VL - 62 IS - 1 SP - 1-32 EP - 1-32 SN - 00222518 KW - Normal form real hypersurface symmetry algebra N2 - We give a complete description of normal forms for real hypersurfaces of finite type in C-2 with respect to their holomorphic symmetry algebras. The normal forms include refined versions of the constructions by Chern-Moser, Stanton, Kolar. We use the method of simultaneous normalisation of the equations and symmetries that goes back to Lie and Cartan. Our approach leads to a unique canonical equation of the hypersurface for every type of its symmetry algebra. Moreover, even in the Levi-degenerate case, our construction implies convergence of the transformation to the normal form if the dimension of the symmetry algebra is at least two. We illustrate our results by explicitly normalising Cartan's homogeneous hypersurfaces and their automorphisms. ER -
EZHOV, Vladimir, Martin KOLÁŘ a Gerd SCHMALZ. Normal Forms and Symmetries of Real Hypersurfaces of Finite Type in C-2. \textit{INDIANA UNIVERSITY MATHEMATICS JOURNAL}. 2013, roč.~62, č.~1, s.~1-32. ISSN~0022-2518.
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