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Extremal Curves in Nilpotent Lie Groups

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, Jyväskylä, 40014, Finland

    Enrico Le Donne

  2. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, via Campi 213/B, 41100, Modena, Italy

    Gian Paolo Leonardi

  3. Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121, Padova, Italy

    Roberto Monti & Davide Vittone

Authors
  1. Enrico Le Donne
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  2. Gian Paolo Leonardi
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  3. Roberto Monti
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  4. Davide Vittone
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Corresponding author

Correspondence to Enrico Le Donne.

Additional information

This work was partially supported by the Fondazione CaRiPaRo Project “Nonlinear Partial Differential Equations: models, analysis, and control-theoretic problems”, Padova.

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Le Donne, E., Leonardi, G.P., Monti, R. et al. Extremal Curves in Nilpotent Lie Groups. Geom. Funct. Anal. 23, 1371–1401 (2013). https://doi.org/10.1007/s00039-013-0226-7

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  • DOI: https://doi.org/10.1007/s00039-013-0226-7

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