Email this article On integrability of certain rank 2 sub-Riemannian structures
- Authors: Kruglikov B.S.1, Vollmer A.2,3, Lukes-Gerakopoulos G.4,5
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Affiliations:
- 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
- Issue: Vol 22, No 5 (2017)
- Pages: 502-519
- Section: Article
- URL: https://ogarev-online.ru/1560-3547/article/view/218699
- DOI: https://doi.org/10.1134/S1560354717050033
- ID: 218699
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Abstract
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.
About the authors
Boris S. Kruglikov
Institute of Mathematics and Statistics
Author for correspondence.
Email: boris.kruglikov@uit.no
Norway, Tromsø, 90-37
Andreas Vollmer
Mathematisches Institut; INdAM - Politecnico di Torino, Dipartimento di Scienze Matematiche
Email: boris.kruglikov@uit.no
Germany, 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
Czech Republic, Prague, 121 16; Boční II 1401/1a, Prague, CZ-141 31
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