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arXiv · 1810.03869

A sub-Finsler problem on the Cartan group

A. Ardentov·E. Le Donne·Yu. Sachkov
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Abstract

In this paper we study a sub-Finsler geometric problem on the free-nilpotent group of rank 2 and step 3. Such a group is also called Cartan group and has a natural structure of Carnot group, which we metrize considering the $\ell_\infty$ norm on its first layer. We adopt the point of view of time-optimal control theory. We characterize extremal curves via Pontryagin maximum principle. We describe abnormal and singular arcs, and construct the bang-bang flow.

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A. Ardentov, E. Le Donne, Yu. Sachkov. 2018-10-09. A sub-Finsler problem on the Cartan group. https://arxiv.org/abs/1810.03869

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