Sub-Riemannian geodesics on the 3-D sphere

2008/04/10 by Der-Chen Chang, Der‐Chen Chang, Chang, Der-Chen +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geodesic #Geodesic map #Geology #Geometric Analysis and Curvature Flows #Geometry #Mathematics #Morphological variations and asymmetry #Physics #Pure mathematics #math.DG #msc:53C17 #msc:70H05

paper · pdf · doi:10.48550/arxiv.0804.1695

published in arXiv (Cornell University) (Cornell University) · 13 pages, 1 figure

openalex publication_date 2008/04/10 · arxiv created 2008/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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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