Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SO}(3)\)

DOI10.1134/S0037446615040047zbMath1327.53033arXiv1507.07221OpenAlexW4235232324WikidataQ115248452 ScholiaQ115248452MaRDI QIDQ748468

I. A. Zubareva, Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 29 October 2015

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

Full work available at URL: https://arxiv.org/abs/1507.07221

zbMATH Keywords

Lie algebraLie groupgeodesicshortest arcleft-invariant sub-Riemannian metric

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 (13)

Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups ⋮ 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 ⋮ 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 ⋮ Sub-Riemannian distance in the Lie groups SU(2) and SO(3) ⋮ Symmetries in left-invariant optimal control problems ⋮ Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems ⋮ Conjugate time in the sub-Riemannian problem on the Cartan group ⋮ Symmetric Riemannian problem on the group of proper isometries of hyperbolic plane ⋮ Homogeneous sub-Riemannian geodesics on a group of motions of the plane ⋮ 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. II
• A metric characterization of Riemannian submersions
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces
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