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
URL:
http://dx.doi.org/10.1007/BF02463257
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