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

DOI10.1134/s0037446623030060zbMath1517.53037arXiv2211.06685MaRDI QIDQ6101504

I. A. Zubareva

Publication date: 1 June 2023

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

Full work available at URL: https://arxiv.org/abs/2211.06685

zbMATH Keywords

Lie algebraLie groupcut locusgeodesicshortest arcleft-invariant sub-Riemannian metricfirst conjugate locus

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Differential geometry of symmetric spaces (53C35) Sub-Riemannian geometry (53C17)

Related Items (1)

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

Cites Work

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• Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SO}(3)\)
• Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions
• Sub-Riemannian distance in the Lie groups SU(2) and SO(3)
• Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups
• Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces

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