We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It turns out that abnormal extremals are precisely the horizontal curves contained in algebraic varieties of a specic type. We also extend the results to the nonfree case.
Extremal Curves in Nilpotent Lie Groups / Le Donne, Enrico; Leonardi, Gian Paolo; Monti, Roberto; Vittone, Davide. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - ELETTRONICO. - 2012, 23:4(2013), pp. 1371-1401. [10.1007/s00039-013-0226-7]
Extremal Curves in Nilpotent Lie Groups
Leonardi Gian Paolo;
2013-01-01
Abstract
We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It turns out that abnormal extremals are precisely the horizontal curves contained in algebraic varieties of a specic type. We also extend the results to the nonfree case.File in questo prodotto:
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