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Extremal Curves in Nilpotent Lie Groups |
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| Authors: | Enrico Le Donne Gian Paolo Leonardi Roberto Monti Davide Vittone |
| Affiliation: | 1. Department of Mathematics and Statistics, University of Jyv?skyl?, P.O. Box 35, Jyv?skyl?, 40014, Finland 2. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, via Campi 213/B, 41100, Modena, Italy 3. Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121, Padova, Italy |
| 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 specific type. We also extend the results to the nonfree case. |
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