HIGHER ORDER SYMMETRIES OF REAL HYPERSURFACES IN C-3
| Authors | |
|---|---|
| Year of publication | 2016 |
| Type | Article in Periodical |
| Magazine / Source | Proceedings of the American Mathematical Society |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1090/proc/13090 |
| Field | General mathematics |
| Keywords | Catlin multitype; Levi degenerate manifold; CR automorphisms |
| Description | 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. |
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