• DocumentCode
    2236279
  • Title

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

  • Author

    Boscain, Ugo ; Rossi, Francesco

  • fYear
    2008
  • fDate
    9-11 Dec. 2008
  • Firstpage
    1280
  • Lastpage
    1284
  • Abstract
    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 Carnot-Caratheodory 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.
  • Keywords
    Lie groups; geometry; 3D simple Lie groups; Carnot-Caratheodory metrics; Cartan decomposition; Heisenberg group; Killing form; conjugate loci; cut loci; nonholonomic constraint; shortest paths; subRiemannian geometry; Algebra; Computational geometry; Geophysics computing; Matrix decomposition; Writing; Carnot-Caratheodory distance; global structure of the cut locus; left-invariant sub-Riemannian geometry;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Decision and Control, 2008. CDC 2008. 47th IEEE Conference on
  • Conference_Location
    Cancun
  • ISSN
    0191-2216
  • Print_ISBN
    978-1-4244-3123-6
  • Electronic_ISBN
    0191-2216
  • Type

    conf

  • DOI
    10.1109/CDC.2008.4738627
  • Filename
    4738627
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2236279