Generalized curvatures in contact sub-Riemannian geometry.

The generalized or control curvatures are intrinsic invariants of Hamiltonian systems. These curvatures were originaly introduced in the framework of the Optimal Control theory by A. Agrachev and R. Gamkrelidze in 1990s. The generalized curvatures extend the notion of sectional curvatures in Riemannian manifolds to a much larger class of problems, including mechanical systems and sub-Riemannian manifolds. In this talk we give a short overwiew of general facts and constructions, and describe more in detail intrinsic curvatures appearing in (2,3) contact sub-Riemannian manifolds.