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

V. Berestovskii; I. Zubareva

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arXiv · 1507.05554

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

V. Berestovskii·I. Zubareva

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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 $(SO_0(2,1),d)$.

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BibTeX RIS

V. Berestovskii, I. Zubareva. 2015-07-20. Sub-Riemannian distance on the Lie group $SO_0(2,1)$. https://arxiv.org/abs/1507.05554

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