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arXiv · 0911.1167

Classification of homogeneous CR-manifolds in dimension 4

V. K. Beloshapka·I. G. Kossovskiy
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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 $\CC{3}$, linearly independent at each point.

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V. K. Beloshapka, I. G. Kossovskiy. 2009-12-09. Classification of homogeneous CR-manifolds in dimension 4. https://arxiv.org/abs/0911.1167

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