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.
Ключевые слова:
Sub-Riemannian geodesic flow, Killing tensor, integral, symmetry, Tanaka prolongation, overdetermined system of PDE, prolongation.
BK and AV were supported by the NFR and DAAD cooperation grant 2014-2015, respectively. AV is a research fellow of Istituto Nazionale di Alta Matematica, a member of GNSAGA, and thanks GRK 1523 (DFG) and the project FIR-2013 Geometria delle equazioni differenziali for financial support. GLG was supported by the UNCE-204020 and GACR-17-06962Y grants.
Поступила в редакцию: 31.01.2017 Принята в печать: 15.08.2017
Образец цитирования:
Boris S. Kruglikov, Andreas Vollmer, Georgios Lukes-Gerakopoulos, “On Integrability of Certain Rank 2 Sub-Riemannian Structures”, Regul. Chaotic Dyn., 22:5 (2017), 502–519
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\paper On Integrability of Certain Rank 2 Sub-Riemannian Structures
\jour Regul. Chaotic Dyn.
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\pages 502--519
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\crossref{https://doi.org/10.1134/S1560354717050033}
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https://www.mathnet.ru/rus/rcd272
https://www.mathnet.ru/rus/rcd/v22/i5/p502
Эта публикация цитируется в следующих 5 статьяx:
Yuriǐ G. Nikonorov, Irina A. Zubareva, “On the behavior of geodesics of left-invariant sub-Riemannian metrics on the group Aff0(R)×Aff0(R)”, era, 33:1 (2025), 181
A. Bravo-Doddoli, E. Le Donne, N. Paddeu, “Symplectic reduction of the sub-Riemannian geodesic flow for metabelian nilpotent groups”, Geom. Mech., 01:01 (2024)
Boris Kruglikov, Wijnand Steneker, “Killing tensors in Koutras–Mcintosh spacetimes”, Class. Quantum Grav., 39:22 (2022), 225005
Alexey Bolsinov, Jinrong Bao, “A Note about Integrable Systems on Low-dimensional Lie Groups and Lie Algebras”, Regul. Chaotic Dyn., 24:3 (2019), 266–280
Цитирование в формате AMSBIB
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