Sub-Riemannian geodesics on the 3-D sphere

2008/04/10 by Der‐Chen Chang, Chang, Der-Chen, Irina Markina +3
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.0804.1695

Abstract

The unit sphere \mathbb S³ 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.

Citations

• Shortest paths for sub-Riemannian metrics on rank-two distributions

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