Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal curves in nilpotent Lie groups   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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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int