%0 Report %D 2013 %T The curvature: a variational approach %A Andrei A. Agrachev %A Davide Barilari %A Luca Rizzi %K Crurvature, subriemannian metric, optimal control problem %X 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. %I SISSA %G en %U http://hdl.handle.net/1963/7226 %1 7260 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-12-03T08:46:32Z No. of bitstreams: 1 1306.5318v3.pdf: 991021 bytes, checksum: f99fb9f1455fa70fbca476e8fd2571af (MD5)