Extremal curves in nilpotent Lie groups
Differential Geometry
2013-07-22 v2 Analysis of PDEs
Group Theory
Metric Geometry
Optimization and Control
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 specific type. We also extend the results to the nonfree case.
Keywords
Cite
@article{arxiv.1207.3985,
title = {Extremal curves in nilpotent Lie groups},
author = {Enrico Le Donne and Gian Paolo Leonardi and Roberto Monti and Davide Vittone},
journal= {arXiv preprint arXiv:1207.3985},
year = {2013}
}
Comments
30 pages, final version