00870nas a2200109   4500008004300000245007800043210006900121520049600190100001700686700002100703856003600724       2008                        en_Ud  00aInvariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces0 aInvariant CarnotCaratheodory metrics on S3 SO3 SL2 and Lens Spac3 aIn 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).1 aBoscain, Ugo1 aRossi, Francesco  uhttp://hdl.handle.net/1963/2144