arXiv:1507.05554 [math.DG]AbstractReferencesReviewsResources
Sub-Riemannian distance on the Lie group $SO_0(2,1)$
Published 2015-07-20Version 1
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 are found for $(SO_0(2,1),d)$.
Comments: 15 pages, 0 figures
Categories: math.DG
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