Homogeneous hypersurfaces in \CC3, associated with a model CR-cubic

2009/10/05 by Beloshapka, V. K., Kossovskiy, I. G.
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.0658

Abstract

The model 4-dimensional CR-cubic in \CC3 has the following "model" property: it is (essentially) the unique locally homogeneous 4-dimensional CR-manifold in \CC3 with finite-dimensional infinitesimal automorphism algebra \mathfrakg and non-trivial isotropy subalgebra. We study and classify, up to local biholomorphic equivalence, all \mathfrakg-homogeneous hypersurfaces in \CC3 and also classify the corresponding local transitive actions of the model algebra \mathfrakg on hypersurfaces in \CC3.

Related

• Homogeneous CR-manifold in ℂ⁴
• Classification of homogeneous CR-manifolds in dimension 4
• Characterization of real-analytic infinitesimal CR automorphisms for a class of hypersurfaces in \Bbb C⁴.
• Homogeneous 2-nondegenerate CR manifolds of hypersurface type in low dimensions
• Totally nondegenerate models and standard manifolds in CR dimension one