Sub-Riemannian distance on the Lie group $SO_0(2,1)$

V. Berestovskii; I. Zubareva

Sub-Riemannian distance on the Lie group $SO_0(2,1)$

Differential Geometry 2015-07-22 v2

Authors: V. Berestovskii , I. Zubareva

Abstract

A left-invariant sub-Riemannian metric $d$ on the shortened Lorentz group $SO_0(2,1)$ under the condition that $d$ is right-invariant relative to the orthogonal Lie subgroup $1\otimes SO(2)$ is studied. The distance between arbitrary two elements, the cut locus (as the union of the subgroup $1\otimes SO(2)$ with the antipodal set to the submanifold of symmetric matrices in the open solid torus $SO_0(2,1)$ ), and the conjugate set for the unit are found for $(SO_0(2,1),d)$ .

Keywords

sub-Riemannian geometry Lie group SO_0(2,1) left-invariant metric right-invariance cut locus conjugate set Lorentz group

Cite

@article{arxiv.1507.05554,
  title  = {Sub-Riemannian distance on the Lie group $SO_0(2,1)$},
  author = {V. Berestovskii and I. Zubareva},
  journal= {arXiv preprint arXiv:1507.05554},
  year   = {2015}
}

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15 pages, 0 figures

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