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

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