Sub-Riemannian cut time and cut locus in Reiter–Heisenberg groups

Abstract

We study the sub-Riemannian cut time and cut locus of a given point in a class of step-2 Carnot groups of Reiter-Heisenberg type. Following the Hamiltonian point of view, we write and analyze extremal curves, getting the cut time of any of them, and a precise description of the set of cut points.