Sub-Riemannian geodesics on the 3-D sphere

Details Sub-Riemannian geodesics on the 3-D sphere Sub-Riemannian geodesics on the 3-D sphere

2008-04-10

arxiv.org/abs/0804.1695v2

Mathematics

Differential Geometry

13 pages, 1 figure

Scientific paper

The unit sphere $\mathbb S^3$ 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 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.

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