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arXiv · 1507.03082

On integrability of certain rank 2 sub-Riemannian structures

Boris Kruglikov·Andreas Vollmer·Georgios Lukes-Gerakopoulos
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Abstract

We discuss the integrability of rank 2 sub-Riemannian structures on low-dimensional manifolds, and then prove that some structures of that type in dimension 6, 7 and 8 have a lot of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing fields and the Hamiltonian, thus indicating non-integrability of the corresponding geodesic flows.

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Boris Kruglikov, Andreas Vollmer, Georgios Lukes-Gerakopoulos. 2015-07-11. On integrability of certain rank 2 sub-Riemannian structures. https://doi.org/10.1134/s1560354717050033

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