Inserted: 17 jul 2012
Last Updated: 4 jul 2013
Journal: GAFA Geometric and Functional Analysis
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.
Keywords: Carnot groups, Regularity of geodesics, Abnormal curves, Extremal curves, Free nilpotent groups, SubRiemannian geometry, Algebraic variety