33 citations
- University of LiverpoolGB6 papers
- Russian Academy of SciencesRU5 papers
- Eindhoven University of TechnologyNL2 papers
- Institute for Systems AnalysisRU2 papers
- Nanjing University of Science and TechnologyCN2 papers
- Scuola Internazionale Superiore di Studi AvanzatiIT2 papers
- University of JyväskyläFI2 papers
- University of PereslavlRU2 papers
- V. A. Trapeznikov Institute of Control SciencesRU2 papers
- Zhejiang Sci-Tech UniversityCN2 papers
- Centre d'Analyse et de Mathématique SocialesFR1 paper
- Centre National de la Recherche ScientifiqueFR1 paper
14 papers · 1 filter
Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures
A. V. Podobryaev
The problem of finding optimal curves (the longest arcs) for sub-Lorentzian structures is an optimal control problem with an unbounded control set and a concave cost functional. Th…
One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2,R)
A. V. Podobryaev
We consider a one-parametric series of left-invariant Lorentzian structures on the universal covering of the Lie group SL(2,R). These structures have SO(1,1)-symmetry and they are…
Existence theorem for sub-Lorentzian problems
L. V. Lokutsievskiy, A. V. Podobryaev
In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We…
Homogeneous geodesics in sub-Riemannian geometry
A. V. Podobryaev
We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic t…
Bicycle paths, elasticae and sub-Riemannian geometry
Andrey Ardentov, Gil Bor, Enrico Le Donne +2
We relate the sub-Riemannian geometry on the group of rigid motions of the plane to `bicycling mathematics'. We show that this geometry's geodesics correspond to bike paths whose f…
Casimir functions of free nilpotent Lie groups of steps three and four
Alexey V. Podobryaev
Any free nilpotent Lie algebra is determined by its rank and step. We consider free nilpotent Lie algebras of steps 3, 4 and corresponding connected and simply connected Lie groups…