Higher order symmetries of real hypersurfaces in \Bbb C³.

2015/08/10 by Kolar, Martin, Meylan, Francine · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.02260

Abstract

We study nonlinear automorphisms of Levi degenerate hypersurfaces of finite multitype. By recent results of Kolar, Meylan and Zaitsev, 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 \mathbb C². We analyze this phenomenon for hypersurfaces of finite Catlin multitype 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 (AIM 2010).

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• New examples of CR submanifolds for the 2-jet determination problem

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