We prove that ideal sub-Riemannian manifolds (ie, admitting no non-trivial abnormal
minimizers) support interpolation inequalities for optimal transport. A key role is played by …

We develop a variational theory of geodesics for the canonical variation of the metric of a
totally geodesic foliation. As a consequence, we obtain comparison theorems for the …

Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds |
Mathematische Annalen Skip to main content Springer Nature Link Account Menu Find a journal …

Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric
structures on manifolds. By a smooth geometric structure on a manifold we mean any …

These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame
of a CIME school. Of course, they contain much more material that I could present in the 6 h …

In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like
invariants. We show that these coefficients can be interpreted as the curvature of a canonical …

We construct differential invariants for generic rank 2 vector distributions on n-dimensional
manifolds, where n⩾ 5. Our method for the construction of invariants is completely different …

We present the classical Wagner construction from 1935 of the curvature tensor for
completely nonholonomic manifolds in both invariant and coordinate way. The starting point …

In 1910 E. Cartan constructed a canonical frame and found the most symmetric case for
maximally non-holonomic rank 2 distributions in ℝ5. We solve the analogous problem for …

The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian
Grassmannian defined up to a symplectic transformation and containing all information …