Sub-Riemannian distance in the Lie groups SU(2) and SO(3)

DOI10.3103/S1055134416020012zbMath1374.53058WikidataQ115223383 ScholiaQ115223383MaRDI QIDQ2959170

I. A. Zubareva, Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 9 February 2017

Published in: Siberian Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Lie algebraLie groupdistancegeodesicinvariant sub-Riemannian metricshortest arc

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) General properties and structure of real Lie groups (22E15) Sub-Riemannian geometry (53C17)

Related Items (11)

Sub-Riemannian distance on the Lie group \(\mathrm{SL}(2)\) ⋮ Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups ⋮ Sub-Riemannian geodesics on SL(2,ℝ) ⋮ Geodesics and curvatures of special sub-Riemannian metrics on Lie groups ⋮ Sub-Riemannian geodesics in \(\mathrm{SO}(3)\) with application to vessel tracking in spherical images of retina ⋮ Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(SU(2)\times{ \mathbb{R} }\) and \(SO(3)\times{ \mathbb{R} }\) with three-dimensional generating distributions ⋮ Almost multiplicity free subgroups of compact Lie groups and polynomial integrability of sub-Riemannian geodesic flows ⋮ 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 ⋮ Tracking of lines in spherical images via sub-Riemannian geodesics in \(\mathrm{SO}(3)\) ⋮ The geodesics of a sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane ⋮ Homogeneous sub-Riemannian geodesics on a group of motions of the plane

Cites Work

• Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric
• Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SO}(3)\)
• A metric characterization of Riemannian submersions
• (Locally) shortest arcs of a special sub-Riemannian metric on the Lie group $\mathrm {SO}_0(2,1)$
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces
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