Sub-Riemannian distance on the Lie group \(\mathrm{SL}(2)\)

DOI10.1134/S0037446617010037zbMath1369.53022arXiv1507.05554OpenAlexW2593052436WikidataQ115248431 ScholiaQ115248431MaRDI QIDQ2360254

I. A. Zubareva, Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 30 June 2017

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05554

zbMATH Keywords

Lie algebraLie groupdistancegeodesicgeodesic orbit spaceinvariant sub-Riemannian metricshortest arc

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Geodesics in global differential geometry (53C22) Sub-Riemannian geometry (53C17)

Related Items (7)

Sub-Riemannian geodesics on SL(2,ℝ) ⋮ 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 ⋮ 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 ⋮ The Schouten curvature tensor and the Jacobi equation in sub-Riemannian geometry ⋮ Homogeneous sub-Riemannian geodesics on a group of motions of the plane ⋮ Sub-Riemannian distance on the Lie group $\operatorname {SO}_0(2,1)$

Cites Work

• Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SL}(2)\)
• Sub-Riemannian distance in the Lie groups SU(2) and SO(3)
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces
• Unnamed Item

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