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

V. Berestovskii; I. Zubareva

paper

Sub-Riemannian distance on the Lie group $S O_{0} (2, 1)$

arXiv:1507.05554

Abstract

A left-invariant sub-Riemannian metric $d$ on the shortened Lorentz group $S O_{0} (2, 1)$ under the condition that $d$ is right-invariant relative to the orthogonal Lie subgroup $1 \otimes S O (2)$ is studied. The distance between arbitrary two elements, the cut locus (as the union of the subgroup $1 \otimes S O (2)$ with the antipodal set to the submanifold of symmetric matrices in the open solid torus $S O_{0} (2, 1)$ ), and the conjugate set for the unit are found for $(S O_{0} (2, 1), d)$ .

15 pages, 0 figures

Sub-Riemannian distance on the Lie group SO0​(2,1)

Abstract

Sub-Riemannian distance on the Lie group $S O_{0} (2, 1)$