Geodesic
Locally isometric coverings of the Lie group $\mathrm{SO}_0(2,1)$ with special sub-Riemannian metric
Sbornik. Mathematics, Tome 207 (2016) no. 9, pp. 1215-1235

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We find geodesics, shortest arcs, conjugate sets, cut loci, and distances on locally isometric coverings of the Lie group $\mathrm{SO}_0(2,1)$ with a left-invariant sub-Riemannian metric which is right-invariant with respect to the Lie subgroup $1\oplus \mathrm{SO}(2)\subset \mathrm{SO}_0(2,1)$. Bibliography: 18 titles.
Keywords: geodesic, geodesic orbit space, invariant sub-Riemannian metric, shortest arc, covering space, weakly symmetric space. 
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     title = {Locally isometric coverings of the {Lie} group $\mathrm{SO}_0(2,1)$ with special {sub-Riemannian} metric},
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V. N. Berestovskii; I. A. Zubareva. Locally isometric coverings of the Lie group $\mathrm{SO}_0(2,1)$ with special sub-Riemannian metric. Sbornik. Mathematics, Tome 207 (2016) no. 9, pp. 1215-1235. http://geodesic.mathdoc.fr/item/SM_2016_207_9_a1/