Model spaces in sub-Riemannian geometry

We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense that any linear isometry of the horizontal tangent spaces is realized by a global isometry. We will show that these spaces have a canonical partial connection defined on their horizontal bundle. However, unlike the Riemannian case, such spaces are not uniquely determined by their curvature and their metric tangent cone. Furthermore, the number of invariants needed to determine model spaces with the same tangent cone is in general greater than one.