Journal article

Higher order symmetries of real hypersurfaces in ℂ³

  • Kolář, Martin Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic
  • Meylan, Francine Department of Mathematics, University of Fribourg, Perolles, Fribourg, Switzerland
Published in:
  • Proceedings of the American Mathematical Society. - 2016, vol. 144, no. 11, p. 4807-4818
English 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 $ \mathbb{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.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
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