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

Francesco Boarotto

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

Differential Geometry 2017-04-05 v2

Authors: Francesco Boarotto

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 $SU(2,1)$ .

Keywords

sub-Riemannian contact structures conformal equivalence Lie groups Heisenberg group conformally flat

Cite

@article{arxiv.1412.2358,
  title  = {Conformal equivalence of sub-Riemannian 3D contact structures on Lie groups},
  author = {Francesco Boarotto},
  journal= {arXiv preprint arXiv:1412.2358},
  year   = {2017}
}

Comments

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

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