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@article{1376677, author = {Kolář, Martin and MeylanandRivier, Francine Antoinette}, article_location = {PROVIDENCE}, article_number = {11}, doi = {http://dx.doi.org/10.1090/proc/13090}, keywords = {Catlin multitype; Levi degenerate manifold; CR automorphisms}, language = {eng}, issn = {0002-9939}, journal = {Proceedings of the American Mathematical Society}, title = {HIGHER ORDER SYMMETRIES OF REAL HYPERSURFACES IN C-3}, volume = {144}, year = {2016} }
TY - JOUR ID - 1376677 AU - Kolář, Martin - Meylan-Rivier, Francine Antoinette PY - 2016 TI - HIGHER ORDER SYMMETRIES OF REAL HYPERSURFACES IN C-3 JF - Proceedings of the American Mathematical Society VL - 144 IS - 11 SP - 4807-4818 EP - 4807-4818 PB - AMER MATHEMATICAL SOC SN - 00029939 KW - Catlin multitype KW - Levi degenerate manifold KW - CR automorphisms N2 - We study nonlinear automorphisms of Levi degenerate hypersurfaces of finite multitype. By results of Kolar, Meylan, and Zaitsev in 2014, the Lie algebra of infinitesimal CR automorphisms may contain a graded component consisting of nonlinear vector fields of arbitrarily high degree, which has no analog in the classical Levi nondegenerate case, or in the case of finite type hypersurfaces in C-2. We analyze this phenomenon for hypersurfaces of finite Catlin multitype with holomorphically nondegenerate models in complex dimension three. The results provide a complete classification of such manifolds. As a consequence, we show on which hypersurfaces 2-jets are not sufficient to determine an automorphism. The results also confirm a conjecture about the origin of nonlinear automorphisms of Levi degenerate hypersurfaces, formulated by the first author for an AIM workshop in 2010. ER -
KOLÁŘ, Martin a Francine Antoinette MEYLAN-RIVIER. HIGHER ORDER SYMMETRIES OF REAL HYPERSURFACES IN C-3. \textit{Proceedings of the American Mathematical Society}. PROVIDENCE: AMER MATHEMATICAL SOC, 2016, roč.~144, č.~11, s.~4807-4818. ISSN~0002-9939. Dostupné z: https://dx.doi.org/10.1090/proc/13090.
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