TY - JOUR
T1 - Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces
JF - SIAM J. Control Optim. 47 (2008) 1851-1878
Y1 - 2008
A1 - Ugo Boscain
A1 - Francesco Rossi
AB - 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).
UR - http://hdl.handle.net/1963/2144
U1 - 2099
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -