Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups

被引：0

作者：

A. P. Mashtakov

Yu. L. Sachkov

机构：

[1] Eindhoven University of Technology,

[2] University of Hradec Králové,undefined

来源：

Differential Equations | 2015年 / 51卷

关键词：

Hamiltonian System; Hamiltonian Vector; Pontryagin Maximum Principle; Casimir Function; Liouville Integrability;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider left-invariant sub-Riemannian problems on three-dimensional unimodular Lie groups. We show that the Hamiltonian system of the Pontryagin maximum principle for such problems is Liouville integrable and even superintegrable (i.e., has four independent integrals, three of which are in involution).

引用

页码：1476 / 1483

页数：7

共 50 条

[1] Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups
Mashtakov, A. P.
Sachkov, Yu. L.
DIFFERENTIAL EQUATIONS, 2015, 51 (11) : 1476 - 1483
[2] Left-invariant hypercontact structures on three-dimensional Lie groups
Giovanni Calvaruso
Antonella Perrone
Periodica Mathematica Hungarica, 2014, 69 : 97 - 108
[3] Left-invariant hypercontact structures on three-dimensional Lie groups
Calvaruso, Giovanni
Perrone, Antonella
PERIODICA MATHEMATICA HUNGARICA, 2014, 69 (02) : 97 - 108
[4] On harmonic tensors on three-dimensional Lie groups with left-invariant Riemannian metric
Gladunova, O. P.
Rodionov, E. D.
Slavskii, V. V.
DOKLADY MATHEMATICS, 2008, 77 (02) : 306 - 309
[5] On harmonic tensors on three-dimensional Lie groups with left-invariant Riemannian metric
O. P. Gladunova
E. D. Rodionov
V. V. Slavskii
Doklady Mathematics, 2008, 77 : 306 - 309
[6] Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric
V. N. Berestovskĭ
Siberian Mathematical Journal, 2014, 55 : 783 - 791
[7] FLAT LEFT-INVARIANT PSEUDO-RIEMANNIAN METRICS ON UNIMODULAR LIE GROUPS
Lebzioui, Hicham
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (04) : 1723 - 1730
[8] Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric
Berestovskii, V. N.
SIBERIAN MATHEMATICAL JOURNAL, 2014, 55 (05) : 783 - 791
[9] THE MODULI SPACES OF LORENTZIAN LEFT-INVARIANT METRICS ON THREE-DIMENSIONAL UNIMODULAR SIMPLY CONNECTED LIE GROUPS
Boucetta, Mohamed
Chakkar, Abdelmounaim
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2022, 59 (04) : 651 - 684
[10] Harmonicity of the Weyl tensor of left-invariant Riemannian metrics on four-dimensional unimodular Lie groups
Gladunova O.P.
Slavskiǐ V.V.
Siberian Advances in Mathematics, 2013, 23 (1) : 32 - 46

← 1 2 3 4 5 →