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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamical and control systems 3 (1997), S. 391-418 
    ISSN: 1573-8698
    Keywords: 58A30 ; 53C22 ; 93B29 ; 49K15 ; Sub-Riemannian geometry ; distributions ; Hamiltonian geodesic ; abnormal geodesic ; nilpotent Lie groups
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Let (M, ε, g) be a sub-Riemannian manifold. The geodesics of (M, ε, g) are either Hamiltonian or srictly abnormal. In this paper we give necessary and sufficient conditions for a geodesic curve to be Hamiltonian, and we apply this to the study of totally geodesic submanifolds of Lie groups. We also give an example of a foliation by totally geodesic submanifolds, each leaf containing a one parameter family of geodesics which are Hamiltonian in the leaf but stricly abnormal in the ambient space.
    Type of Medium: Electronic Resource
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