Sub-Riemannian Geodesics and Shortest Arcs on the Universal Covering of the Full Connected Isometry Group of the Heisenberg Group with Left-Invariant Sub-Riemannian Metric Full article
| Journal |
Proceedings of the Steklov Institute of Mathematics
ISSN: 0081-5438 , E-ISSN: 1531-8605 |
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| Output data | Year: 2026, Volume: 332, Number: 1, Pages: 36-50 Pages count : 15 DOI: 10.1134/s0081543826600365 | ||||
| Tags | exponential map, geodesic, Heisenberg group, homogeneous sub-Riemannian manifold, left-invariant sub-Riemannian metric, Lie algebra, Lie group, modified Grushin plane, submetry. | ||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0033 |
| 2 | Министерство науки и высшего образования РФ | FWNF-2026-0022 |
Abstract:
We discuss integrability questions for some ODE systems. We study the structure of the universal covering Lie group G of the full connected isometry Lie group of the Heisenberg group endowed with a left-invariant sub-Riemannian metric and analyze left-invariant sub-
Riemannian metrics on G. Special attention is paid to the sub-Riemannian metric on G for which geodesics can be expressed in elementary functions. We prove that the geodesic equations for every left-invariant sub-Riemannian metric on G with a two- or three-dimensional vector
subspace V generating the Lie algebra and, in the case dim V = 3, containing the center of the Lie algebra are integrable in quadratures (but not in elementary functions when dim V = 2).
Cite:
Berestovskii V.N.
, Zubareva I.A.
Sub-Riemannian Geodesics and Shortest Arcs on the Universal Covering of the Full Connected Isometry Group of the Heisenberg Group with Left-Invariant Sub-Riemannian Metric
Proceedings of the Steklov Institute of Mathematics. 2026. V.332. N1. P.36-50. DOI: 10.1134/s0081543826600365 WOS Scopus РИНЦ OpenAlex
Sub-Riemannian Geodesics and Shortest Arcs on the Universal Covering of the Full Connected Isometry Group of the Heisenberg Group with Left-Invariant Sub-Riemannian Metric
Proceedings of the Steklov Institute of Mathematics. 2026. V.332. N1. P.36-50. DOI: 10.1134/s0081543826600365 WOS Scopus РИНЦ OpenAlex
Original:
Берестовский В.Н.
, Зубарева И.А.
Субримановы геодезические и кратчайшие на универсальной накрывающей полной связной группы изометрий группы Гейзенберга с левоинвариантной субримановой метрикой
Труды Математического института имени В.А. Стеклова. 2026. Т.332. С.42--56. DOI: 10.4213/tm4537 OpenAlex
Субримановы геодезические и кратчайшие на универсальной накрывающей полной связной группы изометрий группы Гейзенберга с левоинвариантной субримановой метрикой
Труды Математического института имени В.А. Стеклова. 2026. Т.332. С.42--56. DOI: 10.4213/tm4537 OpenAlex
Dates:
| Submitted: | Jun 9, 2025 |
| Accepted: | Mar 24, 2026 |
| Published print: | Jul 23, 2026 |
| Published online: | Jul 23, 2026 |
Identifiers:
| ≡ Web of science: | WOS:001829150200011 |
| ≡ Scopus: | 2-s2.0-105045517604 |
| ≡ Elibrary: | 91841563 |
| ≡ OpenAlex: | W7170137854 |