On integrability of certain rank 2 sub-Riemannian structures

被引：0
|
作者：
Boris S. Kruglikov
Andreas Vollmer
Georgios Lukes-Gerakopoulos
机构：
[1] University of Tromsø,Institute of Mathematics and Statistics
[2] Friedrich-Schiller-Universität,Mathematisches Institut
[3] INdAM - Politecnico di Torino,Institute of Theoretical Physics, Faculty of Mathematics and Physics
[4] Dipartimento di Scienze Matematiche,undefined
[5] Charles University in Prague,undefined
[6] Astronomical Institute of the Academy of Sciences of the Czech Republic,undefined
来源：
Regular and Chaotic Dynamics | 2017年 / 22卷
关键词：
Sub-Riemannian geodesic flow; Killing tensor; integral; symmetry; Tanaka prolongation; overdetermined system of PDE; prolongation; 37J30; 37J60; 70G45; 37J15; 35N10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：502 / 519
页数：17
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