@article {2013,
	title = {The curvature: a variational approach},
	number = {arXiv:1306.5318;},
	year = {2013},
	note = {88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections
  on Finsler manifolds, slow growth distributions, Heisenberg group},
	institution = {SISSA},
	abstract = {The curvature discussed in this paper is a rather far going generalization of
the Riemannian sectional curvature. We define it for a wide class of optimal
control problems: a unified framework including geometric structures such as
Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special
attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces.
Our construction of the curvature is direct and naive, and it is similar to the
original approach of Riemann. Surprisingly, it works in a very general setting
and, in particular, for all sub-Riemannian spaces.},
	keywords = {Crurvature, subriemannian metric, optimal control problem},
	url = {http://hdl.handle.net/1963/7226},
	author = {Andrei A. Agrachev and Davide Barilari and Luca Rizzi}
}
