Andrei Ardentov, Eero Hakavuori, Cut time in the sub-Riemannian problem on the Cartan group

Title: Cut time in the sub-Riemannian problem on the Cartan group
Authors: Andrei Ardentov, Eero Hakavuori
Pages: 23
Abstract:

We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachkov for the sub-Riemannian Cartan problem. Along the proof, we obtain a comparison with the known cut times in the sub-Riemannian Engel group, and a sufficient (generic) condition for the uniqueness of the length minimizer between two points. Hence we reduce the optimal synthesis to solving a certain system of equations in elliptic functions.

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ArXiv ID (ENG): 2107.06730