Address:
Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
Department of Mathematics, University of Fribourg, Chemin du Musée 23, CH 1700 Fribourg
E-mail:
mkolar@math.muni.cz
francine.meylan@unifr.ch
Abstract: In this paper we study infinitesimal CR automorphisms of Levi degenerate hypersurfaces. We illustrate the recent general results of [18], [17], [15], on a class of concrete examples, polynomial models in $\mathbb{C}^3$ of the form $\Im \; w = \Re (P(z) \overline{Q(z)}) $, where $P$ and $Q$ are weighted homogeneous holomorphic polynomials in $z = (z_1, z_2)$. We classify such models according to their Lie algebra of infinitesimal CR automorphisms. We also give the first example of a non monomial model which admits a nonlinear rigid automorphism.
AMSclassification: primary 32V35; secondary 32V40.
Keywords: Levi degenerate hypersurfaces, finite multitype, polynomial models, infinitesimal CR automorphisms.
DOI: 10.5817/AM2017-5-255