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

2014/12/07 by Francesco Boarotto, Boarotto, Francesco
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #math.DG

paper · pdf · doi:10.48550/arxiv.1412.2358

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

openalex publication_date 2014/12/07 · openalex created_date 2016/06/24 · arxiv created 2017/04/04 · arxiv updated 2017/04/05 · openalex updated_date 2026/07/28

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 H₃, 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).

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