Classification of homogeneous CR-manifolds in dimension 4
Complex Variables
2009-12-09 v3
Abstract
Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-equivalence, by E.Cartan. We classify, up to local CR-equivalence, all locally homogeneous CR-manifolds in dimension 4. The classification theorem enables us also to classify all symmetric CR-manifolds in dimension 4, up to local biholomorphic equivalence. We also prove that any 4-dimensional real Lie algebra can be realized as an algebra of affine vector fields in a domain in , linearly independent at each point.
Cite
@article{arxiv.0911.1167,
title = {Classification of homogeneous CR-manifolds in dimension 4},
author = {V. K. Beloshapka and I. G. Kossovskiy},
journal= {arXiv preprint arXiv:0911.1167},
year = {2009}
}
Comments
This is a new version, which includes a claim on realizations of 4-dimensional real Lie algebras and an Appendix with the sphericity inspection for certain homogeneous surfaces in $\mathbb{C}^3$