Geodesic
The Agrachev–Barilari–Boscain Method and Estimates for the Number of Segments of Horizontal Broken Lines Joining Points in the Canonical Carnot Group $G_{3,3}$
Informatics and Automation, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 108-117

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Using a generalization of the Agrachev–Barilari–Boscain method for proving the Rashevskii–Chow theorem, we estimate the minimum number $\mathcal {N}_{G_{3,3}}$ of segments of horizontal broken lines joining two arbitrary points on the six-dimensional two-step canonical Carnot group $G_{3,3}$ with corank $3$ horizontal distribution. We prove that $\mathcal {N}_{G_{3,3}}=3$.
Keywords: canonical Carnot group, Rashevskii–Chow theorem, horizontal broken line. 
A. V. Greshnov. The Agrachev–Barilari–Boscain Method and Estimates for the Number of Segments of Horizontal Broken Lines Joining Points in the Canonical Carnot Group $G_{3,3}$. Informatics and Automation, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 108-117. http://geodesic.mathdoc.fr/item/TRSPY_2023_321_a6/
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