Email this article Explicit formulae for extremals in sub-Lorentzian and Finsler problems on 2D and 3D Lie groups
- Authors: Ladeishchikov E.A.1, Lokutsievskiy L.V.2, Prilepin N.V.1
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Affiliations:
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
- Issue: Vol 216, No 12 (2025)
- Pages: 79-124
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/358685
- DOI: https://doi.org/10.4213/sm10355
- ID: 358685
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Abstract
Questions relating to the search of geodesics in a series of left-invariant problems with sub-Lorentzian and Finsler structure are under consideration. Explicit formulae for extremals are found in terms of trigonometric functions of convex trigonometry. In sub-Lorentzian problems the machinery of the new trigonometric functions $\sinh_\Omega$ and $\cosh_\Omega$ , generalizing $\sinh$ and $\cosh$ to the case of an unbounded convex set $\Omega\subset\mathbb R^2$ , is particularly useful.
About the authors
Evgeny Aleksandrovich Ladeishchikov
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Email: evgen310864@gmail.com
without scientific degree, no status
Lev Vyacheslavovich Lokutsievskiy
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Email: lion.lokut@gmail.com
ORCID iD: 0000-0002-8083-4296
Scopus Author ID: 35148203500
ResearcherId: ABE-7153-2021
Doctor of physico-mathematical sciences, no status
Nikita Vladimirovich Prilepin
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Email: nickprilepin@yandex.ru
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