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

DOI10.1134/s003744662402006xarXiv2306.03945MaRDI QIDQ6203332

I. A. Zubareva

Publication date: 27 March 2024

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

Full work available at URL: https://arxiv.org/abs/2306.03945

zbMATH Keywords

Lie algebraLie groupcut locusgeodesicleft-invariant sub-Riemannian metricfirst conjugate locusshortest Arc

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Geodesics in global differential geometry (53C22) Sub-Riemannian geometry (53C17)

Cites Work

• Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SL}(2)\)
• Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions
• Sub-Riemannian distance on the Lie group \(\mathrm{SL}(2)\)
• (Locally) shortest arcs of a special sub-Riemannian metric on the Lie group $\mathrm {SO}_0(2,1)$
• 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
• Sub-Riemannian distance on the Lie group $\operatorname {SO}_0(2,1)$
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces
• 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
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