Abstract.
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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to Björn Gustafsson on the occasion of his 60th birthday
Submitted: June 3, 2008. Accepted: July 12, 2008.
The first author is partially supported by a research grant from the United State Army Research Office and a Hong Kong RGC competitive earmarked research grant #600607. The second and the third authors have been supported by the grant of the Norwegian Research Council #177355/V30, and by the European Science Foundation Research Networking Programme HCAA.
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Chang, DC., Markina, I. & Vasil’ev, A. Sub-Riemannian Geodesics on the 3-D Sphere. Complex Anal. Oper. Theory 3, 361–377 (2009). https://doi.org/10.1007/s11785-008-0089-3
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DOI: https://doi.org/10.1007/s11785-008-0089-3