The normal sub-Riemannian geodesic flow on E(2) generated by a left-invariant metric and a right-invariant distribution

被引：0

作者：

A. D. Mazhitova

机构：

[1] Al-Farabi Kazakh National University,

来源：

Siberian Mathematical Journal | 2014年 / 55卷

关键词：

sub-Riemannian geometry; right-invariant metric; Hamiltonian; geodesic;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider a sub-Riemannian problem on the three-dimensional solvable Lie group E(2) endowed with a left-invariant metric and a right-invariant distribution. The problem is based on construction of a Hamilton structure for the given metric by the Pontryagin maximum principle.

引用

页码：948 / 953

页数：5

共 37 条

[1] The normal sub-Riemannian geodesic flow on E(2) generated by a left-invariant metric and a right-invariant distribution
Mazhitova, A. D.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2014, 55 (05) : 948 - 953
[2] Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric
V. N. Berestovskĭ
[J]. Siberian Mathematical Journal, 2014, 55 : 783 - 791
[3] Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric
Berestovskii, V. N.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2014, 55 (05) : 783 - 791
[4] LEFT-INVARIANT SUB-RIEMANNIAN ENGEL STRUCTURES: ABNORMAL GEODESICS AND INTEGRABILITY
Beschastnyi, Ivan
Medvedev, Alexandr
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2018, 56 (05) : 3524 - 3537
[5] ON LEFT-INVARIANT EINSTEIN RIEMANNIAN METRICS THAT ARE NOT GEODESIC ORBIT
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[J]. TRANSFORMATION GROUPS, 2019, 24 (02) : 511 - 530
[6] ON LEFT-INVARIANT EINSTEIN RIEMANNIAN METRICS THAT ARE NOT GEODESIC ORBIT
YU. G. NIKONOROV
[J]. Transformation Groups, 2019, 24 : 511 - 530
[7] ON THE GEODESIC FLOW ON THE GROUP OF DIFFEOMORPHISMS OF THE CIRCLE WITH A FRACTIONAL SOBOLEV RIGHT-INVARIANT METRIC
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[J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2010, 17 (01) : 7 - 11
[8] On the Geodesic Flow on the Group of Diffeomorphisms of the Circle with a Fractional Sobolev Right-Invariant Metric
Marcus Wunsch
[J]. Journal of Nonlinear Mathematical Physics, 2010, 17 : 7 - 11
[9] Integrability of left-invariant sub-Riemannian structures on the special linear group SL 2(R)
Mashtakov, A. P.
Sachkov, Yu L.
[J]. DIFFERENTIAL EQUATIONS, 2014, 50 (11) : 1541 - 1547
[10] Integrability of left-invariant sub-Riemannian structures on the special linear group SL2(R)
A. P. Mashtakov
Yu. L. Sachkov
[J]. Differential Equations, 2014, 50 : 1541 - 1547

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