On the behavior of geodesics of left-invariant sub-Riemannian metrics on the group Aff0(R) х Aff0(R) Full article
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Electronic Research Archive
, E-ISSN: 2688-1594 |
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| Output data | Year: 2025, Volume: 33, Number: 1, Pages: 181-209 Pages count : 29 DOI: 10.3934/era.2025010 | ||||
| Tags | extremal; generating subspace of a Lie algebra; Hamiltonian system; Kovalevskaya exponents; left-invariant sub-Riemannian metric; non-commutative two-dimensional Lie group; sub-Riemannian geodesic | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН». | FWNF-2022-0003 |
Abstract:
In this paper, we study geodesics of left-invariant sub-Riemannian metrics on the Cartesian square of a connected two-dimensional non-commutative Lie group, where the metric is determined by the inner product on a two-dimensional generating subspace of the corresponding Lie algebra. It is proven that the system of equations for geodesics of such a sub-Riemannian metric is not completely integrable in the class of meromorphic functions. Important qualitative characteristics of the corresponding geodesics are found, thus proving the complexity of their behavior in general.
Cite:
Nikonorov Y.G.
, Zubareva I.A.
On the behavior of geodesics of left-invariant sub-Riemannian metrics on the group Aff0(R) х Aff0(R)
Electronic Research Archive. 2025. V.33. N1. P.181-209. DOI: 10.3934/era.2025010 WOS Scopus РИНЦ OpenAlex
On the behavior of geodesics of left-invariant sub-Riemannian metrics on the group Aff0(R) х Aff0(R)
Electronic Research Archive. 2025. V.33. N1. P.181-209. DOI: 10.3934/era.2025010 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Nov 18, 2024 |
| Accepted: | Jan 2, 2025 |
| Published print: | Jan 20, 2025 |
| Published online: | Jan 20, 2025 |
Identifiers:
| Web of science: | WOS:001423575000001 |
| Scopus: | 2-s2.0-85216865587 |
| Elibrary: | 81143192 |
| OpenAlex: | W4406605941 |
Citing:
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