English

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

Complex Variables 2023-05-16 v1

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 CRCR automorphisms of a model hypersurface M0M_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,P, QQ and RR are homogeneous polynomials. In particular, we classify M0M_0 with respect to the description of its nilpotent rotations when P,P, QQ and RR are monomials. We also give an example of a model M0M_0 for which the real dimension of its generalized (exotic) rotations is 3.3.

Keywords

Cite

@article{arxiv.2305.07757,
  title  = {Characterization of real-analytic infinitesimal CR automorphisms for a class of hypersurfaces in $\Bbb C^4.$},
  author = {Cyril Julien and Francine Meylan},
  journal= {arXiv preprint arXiv:2305.07757},
  year   = {2023}
}