Sub-Riemannian geodesics on the 3-D sphere

Chang, Der-Chen; Markina, Irina; Vasil'ev, Alexander

Sub-Riemannian geodesics on the 3-D sphere

Authors

Chang, Der-Chen

Markina, Irina

Vasil'ev, Alexander

Description

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.
13 pages, 1 figure