Classification of homogeneous CR-manifolds in dimension 4

Details Classification of homogeneous CR-manifolds in dimension 4 Classification of homogeneous CR-manifolds in dimension 4

2009-11-06

arxiv.org/abs/0911.1167v3

Mathematics

Complex Variables

This is a new version, which includes a claim on realizations of 4-dimensional real Lie algebras and an Appendix with the sphe

Scientific paper

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 $\CC{3}$, linearly independent at each point.

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