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CDC
2008
IEEE

Shortest paths on 3-D simple Lie groups with nonholonomic constraint

13 years 10 months ago
Shortest paths on 3-D simple Lie groups with nonholonomic constraint
— In this paper we study the Carnot-Caratheodory metrics on SU(2) S3 , SO(3) and SL(2) induced by their Cartan decomposition and by the Killing form. Besides computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the CarnotCaratheodory distance as the inverse of an elementary function. For SU(2) the cut locus is a maximal circle without one point. In all other cases the cut locus is a stratified set. To our knowledge, this is the first explicit computation of the whole cut locus in sub-Riemannian geometry, except for the trivial case of the Heisenberg group.
Ugo V. Boscain, Francesco Rossi
Added 29 May 2010
Updated 29 May 2010
Type Conference
Year 2008
Where CDC
Authors Ugo V. Boscain, Francesco Rossi
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