Geodesic
A Sub-Finsler Problem on the Cartan Group
Informatics and Automation, Optimal control and differential equations, Tome 304 (2019), pp. 49-67.

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We study a sub-Finsler geometric problem on the free nilpotent group of rank $2$ and step $3$. Such a group is also called the Cartan group and has a natural structure of Carnot group, which we metrize by 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 the Pontryagin maximum principle. We describe abnormal and singular arcs and construct the bang–bang flow. 
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A. A. Ardentov; E. Le Donne; Yu. L. Sachkov. A Sub-Finsler Problem on the Cartan Group. Informatics and Automation, Optimal control and differential equations, Tome 304 (2019), pp. 49-67. http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a3/

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