(Locally) shortest arcs of a special sub-Riemannian metric on the Lie group $\mathrm {SO}_0(2,1)$

DOI10.1090/spmj/1373zbMath1335.53038arXiv1410.1525OpenAlexW2962814156WikidataQ115280833 ScholiaQ115280833MaRDI QIDQ2786966

Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 24 February 2016

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1525

zbMATH Keywords

Lie algebracut locusgeodesicconjugate setshortest arcleft-invariant sub-Riemannian metricLie group \(\mathrm{SO}(2,1)\)

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Existence theories for optimal control problems involving ordinary differential equations (49J15) Sub-Riemannian geometry (53C17)

Related Items (11)

Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SL}(2)\) ⋮ Geodesics and curvatures of special sub-Riemannian metrics on Lie groups ⋮ Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions ⋮ Left-invariant Riemannian problems on the groups of proper motions of hyperbolic plane and sphere ⋮ Locally isometric coverings of the Lie group $ \mathrm{SO}_0(2,1)$ with special sub-Riemannian metric ⋮ Sub-Riemannian distance in the Lie groups SU(2) and SO(3) ⋮ Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(\operatorname{SU}(1,1)\times \mathbb{R}\) and \(\operatorname{SO}_0(2,1)\times \mathbb{R}\) with three-dimensional generating distributions ⋮ Symmetric Riemannian problem on the group of proper isometries of hyperbolic plane ⋮ Homogeneous sub-Riemannian geodesics on a group of motions of the plane ⋮ Sub-Riemannian distance on the Lie group $\operatorname {SO}_0(2,1)$ ⋮ Homogeneous geodesics in sub-Riemannian geometry

Cites Work

• Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric
• On the differential geometry of tangent bundles of Riemannian manifolds
• A metric characterization of Riemannian submersions
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