Extremal curves in nilpotent Lie groups

Enrico Le Donne; Gian Paolo Leonardi; Roberto Monti; Davide Vittone

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arXiv · 1207.3985

Extremal curves in nilpotent Lie groups

Enrico Le Donne·Gian Paolo Leonardi·Roberto Monti·Davide Vittone

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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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BibTeX RIS

Enrico Le Donne, Gian Paolo Leonardi, Roberto Monti, Davide Vittone. 2013-07-19. Extremal curves in nilpotent Lie groups. https://arxiv.org/abs/1207.3985

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