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.
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