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 (Q6101504)
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scientific article; zbMATH DE number 7690976
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 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 |
scientific article; zbMATH DE number 7690976 |
Statements
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 (English)
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1 June 2023
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The author considers the Lie groups \(\mathrm{SU}(2)\times\mathbb{R}\) and \(\mathrm{SO}(3)\times\mathbb{R}\) and studies their sub-Riemannian geometry. More precisely, she obtains geodesics, shortest arcs, cut loci, first conjugate loci, and distances between arbitrary elements for certain left-invariant sub-Riemannian metrics in these Lie groups.
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geodesic
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left-invariant sub-Riemannian metric
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Lie algebra
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Lie group
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shortest arc
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cut locus
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first conjugate locus
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