The Liouville theorem for conformal mappings on Carnot groups with Goursat–Darboux distribution

Under minimal assumptions on smoothness we prove the Liouville theorem on conformal mappings for one infinite series of Carnot groups $\mathbb J^k$ with sub-Riemannian metric with Goursat–Darboux distribution, $k\ge2$: each mapping with $1$-bounded distortion of a connected domain $U$ on $\mathbb J^k$ is equal to the restriction to $U$ of the action of an element of the finite-dimensional group of $1$-quasiconformal smooth mappings.