Sub-Riemannian Geodesics on the 3-D Sphere

被引：12

作者：

Chang, Der-Chen ^{[1
]}

Markina, Irina ^{[2
]}

Vasil'ev, Alexander ^{[2
]}

机构：

[1] Georgetown Univ, Dept Math, Washington, DC 20057 USA

[2] Univ Bergen, Dept Math, N-5008 Bergen, Norway

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2009年 / 3卷 / 02期

关键词：

Sub-Riemannian geometry; geodesic; Hamiltonian system;

D O I：

10.1007/s11785-008-0089-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The unit sphere S(3) can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding Lie algebra de. ne a 2-step sub-Riemannian manifold. We study sub-Riemannian geodesics on this sub-Riemannian manifold making use of the Hamiltonian formalism and solving the corresponding Hamiltonian system.

引用

页码：361 / 377

页数：17

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