期刊
GEOMETRIC AND FUNCTIONAL ANALYSIS
卷 23, 期 4, 页码 1371-1401出版社
SPRINGER BASEL AG
DOI: 10.1007/s00039-013-0226-7
关键词
Regularity of geodesics; abnormal curves; extremal curves; free nilpotent groups; Carnot groups; sub-Riemannian geometry; algebraic variety
类别
资金
- Fondazione CaRiPaRo Project Nonlinear Partial Differential Equations: models, analysis, and control-theoretic problems, Padova
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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