Curvature: a variational approach

Abstract : The curvature discussed in this paper is a rather far going generalization of the Riemann 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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Contributor : Davide Barilari <>
Submitted on : Tuesday, June 25, 2013 - 8:46:00 AM
Last modification on : Wednesday, October 16, 2019 - 1:23:54 AM

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Andrei Agrachev, Davide Barilari, Luca Rizzi. Curvature: a variational approach. Memoirs of the American Mathematical Society, American Mathematical Society, In press, 256 (1225), ⟨10.1090/memo/1225⟩. ⟨hal-00838195⟩



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