Sub-Riemannian geodesics on the 3-D sphere
نویسندگان
چکیده
The unit sphere S 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. Mathematics Subject Classification (2000). Primary: 53C17; Secondary: 70H05 .
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