Sub-Riemannian geodesics on the 3-D sphere
Differential Geometry
2008-06-03 v2
Abstract
The unit sphere 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 define 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.
Cite
@article{arxiv.0804.1695,
title = {Sub-Riemannian geodesics on the 3-D sphere},
author = {Der-Chen Chang and Irina Markina and Alexander Vasil'ev},
journal= {arXiv preprint arXiv:0804.1695},
year = {2008}
}
Comments
13 pages, 1 figure