On sub-Riemannian geodesics on the Engel groups: Hamilton's equations

被引：6

作者：

Adams, Malcolm R. ^{[1
]}

Tie, Jingzhi ^{[1
]}

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

来源：

MATHEMATISCHE NACHRICHTEN | 2013年 / 286卷 / 14-15期

关键词：

Engel groups; Heisenberg groups; Martinet vector fields; Hamiltonian formalism; sub-Riemannian geodesics; elliptic integrals;

D O I：

10.1002/mana.201200259

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the sub-Riemannian geometry on the Engel group which is a step 3 nilpotent Lie group on R4. Our main result is to solve the Hamiltonian equations associated with the bi-characteristic curves and express the solutions in terms of elliptic functions. Our model covers both the Heisenberg group and the Martinet case when setting certain parameters to be zero.

引用

页码：1381 / 1406

页数：26

共 50 条

[21] Characterizations of Hamiltonian geodesics in sub-Riemannian geometry
Laboratoire de Mathématiques, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac, Cedex, France
J Dyn Control Syst, 3 (391-418):
[22] Shortest and straightest geodesics in sub-Riemannian geometry
Alekseevsky, Dmitri
JOURNAL OF GEOMETRY AND PHYSICS, 2020, 155
[23] THE PROBLEM OF GEODESICS IN SINGULAR SUB-RIEMANNIAN GEOMETRY
PELLETIER, F
BOUCHE, LV
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1993, 317 (01): : 71 - 76
[24] Sub-Riemannian Geometry and Geodesics in Banach Manifolds
Arguillere, Sylvain
JOURNAL OF GEOMETRIC ANALYSIS, 2020, 30 (03) : 2897 - 2938
[25] Helical CR structures and sub-Riemannian geodesics
D'Angelo, John P.
Tyson, Jeremy T.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2009, 54 (3-4) : 205 - 221
[26] Sub-Riemannian Geodesics on Nested Principal Bundles
Godoy Molina, Mauricio
Markina, Irina
CONTROLO 2020, 2021, 695 : 82 - 92
[27] Stochastic sub-Riemannian geodesics on the Grushin distribution
Calin, Ovidiu
Udriste, Constantin
Tevy, Ionel
BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 2014, 19 (02): : 37 - 49
[28] Sub-Riemannian Geometry and Geodesics in Banach Manifolds
Sylvain Arguillère
The Journal of Geometric Analysis, 2020, 30 : 2897 - 2938
[29] Cut Locus in the Sub-Riemannian Problem on Engel Group
A. A. Ardentov
Yu. L. Sachkov
Doklady Mathematics, 2018, 97 : 82 - 85
[30] Cut Locus in the Sub-Riemannian Problem on Engel Group
Ardentov, A. A.
Sachkov, Yu. L.
DOKLADY MATHEMATICS, 2018, 97 (01) : 82 - 85

← 1 2 3 4 5 →