(Locally) shortest arcs of special sub-Riemannian metric on the Lie group $S{O}_0(2,1)$

Abstract

The author finds geodesics, shortest arcs, cut locus, and conjugate sets for left-invariant sub-Riemannian metric on the Lie group $S{O}_0(2,1)$ under the condition that the metric is right-invariant relative to the Lie subgroup $SO(2)\subset S{O}_0(2,1)$.

arXiv comment16 pages. arXiv admin note: substantial text overlap with arXiv:1410.1251