Sciact
  • EN
  • RU

On the behavior of geodesics of left-invariant sub-Riemannian metrics on the group Aff0(R) х Aff0(R) Full article

Journal Electronic Research Archive
, E-ISSN: 2688-1594
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 Nikonorov Yuriĭ G. 1 , Zubareva Irina A. 2
Affiliations
1 Southern Mathematical Institute of VSC RAS, Vladikavkaz 362025, Russia
2 Omsk Department of Sobolev Institute of Mathematics of SB RAS, Omsk 644099, Russia

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
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: Пока нет цитирований
Altmetrics: