Conformal equivalence of sub-Riemannian 3D contact structures on Lie groups

Abstract

In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group ${\mathbb{H}}_3$, or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

arXiv commentarXiv admin note: text overlap with arXiv:1007.4970 by other authors, v2. Bibliography expanded and added some further references

Cited by in corpus (1)

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