Sub-Riemannian manifolds as limits of Riemannian manifolds (Q1264839)

A sub-Riemannian metric on a manifold \(M\) is given by a smooth completely non-integrable distribution \(V\) on \(M\) and a smooth Riemannian metric \(g\) on \(V\). The paper gives a survey on geometric properties of such metrics. The central points of view is the approximation of a sub-Riemannian metric by smooth Riemannian metrics in the Gromov-Hausdorff-sense. It is shown that the geodesic equations approximate in a suitable sense. Moreover, geometric properties of the approximating metrics like diameter, volume and injectivity radius are discussed.