@article {2008,
	title = {Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces},
	journal = {SIAM J. Control Optim. 47 (2008) 1851-1878},
	number = {SISSA;58/2007/M},
	year = {2008},
	abstract = {In this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).},
	doi = {10.1137/070703727},
	url = {http://hdl.handle.net/1963/2144},
	author = {Ugo Boscain and Francesco Rossi}
}
