A Formula for Popp’s Volume in Sub-Riemannian Geometry

As an application, we prove a version of sub-Riemannian Bonnet − Myers theorem and we obtain some new results on conjugate points for three dimensional left-invariant

Our construction works under quite general assumptions, satisfied by any sub-Riemannian structure associated with a Riemannian foliation with totally geodesic leaves (e.g. CR and

We will use the fact that we have a clear idea of what Ricci curvature is on a Riemannian manifold, to introduce a corresponding tensor on a sub-Riemannian manifold with

As an application, we prove a version of sub-Riemannian Bonnet-Myers the- orem and we obtain some new results on conjugate points for three dimensional left-invariant

Key-words: sub-Riemannian geometry, Martinet, abnormal geodesi, sympleti integrator, bakward

Using this representation technique, we produce formulas for fundamen- tal Riemannian-geometric objects on the Grassmann manifold endowed with its canonical metric: gradient,

A Riemannian space is a smooth manifold whose tangent spaces are endowed with Euclidean structures; each tangent space is equipped with its own Euclidean structure that smoothly

We define strong right-invariant sub-Riemannian structures on these groups, and we establish the metric and geodesic completeness for the corresponding sub-Riemannian distance;