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Keywords:
Levi degenerate hypersurfaces; finite multitype; polynomial models; infinitesimal CR automorphisms
Levi degenerate hypersurfaces; finite multitype; polynomial models; infinitesimal CR automorphisms
Summary:
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.
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