Abstract In the free, step-2, rank-4 sub-Riemannian Carnot group F₄ F 4, we give a clean expression for length-extremals, we provide an explicit equation for conjugate points, we relate it with the conjectured cut locus of the origin Cut (F₄) Cut (F 4). Finally, we give some upper estimates for the cut-time of extremals.
Montanari et al. (Sat,) studied this question.