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arXiv · 2305.07757

Characterization of real-analytic infinitesimal CR automorphisms for a class of hypersurfaces in $\Bbb C^4.$

Cyril Julien·Francine Meylan
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Abstract

In this paper, motivated by the work of Kim and Kolar for the case of pseudoconvex models which are sums of squares of polynomials, we study the Lie algebra of real-analytic infinitesimal $CR$ automorphisms of a model hypersurface $M_0$ given by \begin{equation} M_0= \{(z,w) \in \mathbb C^{3} \times \mathbb C \ | \ \Im w= P\bar Q + Q\bar P + R\bar R \}, \end{equation} where $P,$ $Q$ and $R$ are homogeneous polynomials. In particular, we classify $M_0$ with respect to the description of its nilpotent rotations when $P,$ $Q$ and $R$ are monomials. We also give an example of a model $M_0$ for which the real dimension of its generalized (exotic) rotations is $3.$

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Cyril Julien, Francine Meylan. 2023-05-12. Characterization of real-analytic infinitesimal CR automorphisms for a class of hypersurfaces in $\Bbb C^4.$. https://arxiv.org/abs/2305.07757

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