On Integrability of Certain Rank 2 Sub-Riemannian Structures

被引：3

作者：

Kruglikov, Boris S. ^{[1
]}

Vollmer, Andreas ^{[2
,3
]}

Lukes-Gerakopoulos, Georgios ^{[4
,5
]}

机构：

[1] Univ Tromso, Inst Math & Stat, N-9037 Tromso, Norway

[2] Friedrich Schiller Univ, Math Inst, D-07737 Jena, Germany

[3] Politecn Torino, Dipartimento Sci Matemat, INdAM, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[4] Charles Univ Prague, Fac Math & Phys, Inst Theoret Phys, Prague 12116, Czech Republic

[5] Acad Sci Czech Republ, Astron Inst, Bocni 2 1401-1A, CZ-14131 Prague, Czech Republic

来源：

REGULAR & CHAOTIC DYNAMICS | 2017年 / 22卷 / 05期

关键词：

Sub-Riemannian geodesic flow; Killing tensor; integral; symmetry; Tanaka prolongation; overdetermined system of PDE; prolongation; GEODESIC-FLOWS; DISTRIBUTIONS; EQUATIONS; GEOMETRY;

D O I：

10.1134/S1560354717050033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：502 / 519

页数：18

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