Отправить статью по E-mail On integrability of certain rank 2 sub-Riemannian structures
- Авторы: Kruglikov B.S.1, Vollmer A.2,3, Lukes-Gerakopoulos G.4,5
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Учреждения:
- Institute of Mathematics and Statistics
- Mathematisches Institut
- INdAM - Politecnico di Torino, Dipartimento di Scienze Matematiche
- Institute of Theoretical Physics, Faculty of Mathematics and Physics
- Astronomical Institute of the Academy of Sciences of the Czech Republic
- Выпуск: Том 22, № 5 (2017)
- Страницы: 502-519
- Раздел: Article
- URL: https://journals.rcsi.science/1560-3547/article/view/218699
- DOI: https://doi.org/10.1134/S1560354717050033
- ID: 218699
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Аннотация
We discuss rank 2 sub-Riemannian structures on low-dimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the Hamiltonian, thus indicating nonintegrability of the corresponding geodesic flows.
Об авторах
Boris Kruglikov
Institute of Mathematics and Statistics
Автор, ответственный за переписку.
Email: boris.kruglikov@uit.no
Норвегия, Tromsø, 90-37
Andreas Vollmer
Mathematisches Institut; INdAM - Politecnico di Torino, Dipartimento di Scienze Matematiche
Email: boris.kruglikov@uit.no
Германия, Jena, 07737; Corso Duca degli Abruzzi 24, Torino, 10129
Georgios Lukes-Gerakopoulos
Institute of Theoretical Physics, Faculty of Mathematics and Physics; Astronomical Institute of the Academy of Sciences of the Czech Republic
Email: boris.kruglikov@uit.no
Чехия, Prague, 121 16; Boční II 1401/1a, Prague, CZ-141 31
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