Extremal curves in nilpotent Lie groups

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

arxiv: 1207.3985 · v2 · pith:HFXQJGOOnew · submitted 2012-07-17 · 🧮 math.DG · math.AP· math.GR· math.MG· math.OC

Extremal curves in nilpotent Lie groups

Enrico Le Donne , Gian Paolo Leonardi , Roberto Monti , Davide Vittone This is my paper

classification 🧮 math.DG math.APmath.GRmath.MGmath.OC

keywords curvesextremalgroupsnilpotentabnormaladjointalgebraiccase

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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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Extremal curves in nilpotent Lie groups

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