Nonlinear CR automorphisms of Levi degenerate hypersurfaces and a new gap phenomenon

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Authors	KOLÁŘ Martin MEYLAN-RIVIER Francine Antoinette
Year of publication	2019
Type	Article in Periodical
Magazine / Source	ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE
MU Faculty or unit	Faculty of Science
Citation
Web	http://annaliscienze.sns.it/public/pdf/abstracts/2019/02_KOLAR_etal_ab.pdf
Doi	http://dx.doi.org/10.2422/2036-2145.201703_016
Keywords	CHERN-MOSER OPERATORS; REAL HYPERSURFACES; FINITE-TYPE; JET DETERMINATION; SYMMETRIES; RIGIDITY
Description	We give a complete classification of polynomial models for smooth real hypersurfaces of finite Catlin multitype in C-3, which admit nonlinear infinitesimal CR automorphisms. As a consequence, we obtain a sharp 1-jet determination result for any smooth hypersurface with such a model. The results also prove a conjecture of the first author about the origin of such nonlinear automorphisms (AIM list of problems, 2010). As another consequence, we describe all possible dimensions of the Lie algebra of infinitesimal CR automorphisms, which leads to a new "secondary" gap phenomenon.
Related projects:	Klasifikační problémy pro reálné nadplochy v komplexním prostoru