Nilpotent \((3, 6)\) sub-Riemannian problem. (English) Zbl 1047.93014

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.


93B29 Differential-geometric methods in systems theory (MSC2000)
53C17 Sub-Riemannian geometry
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