Browsing by Author "Barilari, Davide"

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    The curvature: a variational approach
    (SISSA, 2013-06-22) Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca; Mathematics
    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.
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    Introduction to Riemannian and sub-Riemannian geometry
    (SISSA, 2012-04) Agrachev, Andrei A.; Barilari, Davide; Boscain, Ugo; Mathematics; Functional Analysis and Applications