Nilpotent \((3, 6)\) sub-Riemannian problem (Q1850875)

The paper characterizes the set of points where the sub-Riemannian geodesics originating from a given point lose optimality, in the case of a \((3,6)\) sub-Riemannian manifold. It turns out that this set coincides with the first caustic, which admits a simple representation. The author conjectures that a similar result possibly holds for all \((n, \frac{n(n+1)}{2})\) sub-Riemanian problems.