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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 and Francine Antoinette MEYLAN-RIVIER. HIGHER ORDER SYMMETRIES OF REAL HYPERSURFACES IN C-3. \textit{Proceedings of the American Mathematical Society}. PROVIDENCE: AMER MATHEMATICAL SOC, vol.~144, No~11, p.~4807-4818. ISSN~0002-9939. doi:10.1090/proc/13090. 2016.
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