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2013•Institutional Research Information System (Università degli Studi di Trento)Open access

Extremal Curves in Nilpotent Lie Groups

LE DONNE ENRICO, Leonardi Gian Paolo, MONTI ROBERTO, VITTONE DAVIDE

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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 specic type. We also extend the results to the nonfree case.

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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 specic type. We also extend the results to the nonfree case.

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Available 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.

Key concepts: Mathematics, Pontryagin's minimum principle, Nilpotent, Lie group, Pure mathematics, Adjoint representation, Lie algebra, Lie theory

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