Locally isometric coverings of the Lie group $\mathrm{SO}_0(2,1)$ with special sub-Riemannian metric

V. N. Berestovskii   ; I. A. Zubareva

Sbornik. Mathematics, Tome 207 (2016) no. 9, pp. 1215-1235

Résumé

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.

Détail

Keywords: geodesic, geodesic orbit space, invariant sub-Riemannian metric, shortest arc, covering space, weakly symmetric space.

Bibliographie

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