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Journal Articles Memoirs of the American Mathematical Society Year : 2019

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.

Dates and versions

hal-00838195 , version 1 (25-06-2013)

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Andrei Agrachev, Davide Barilari, Luca Rizzi. Curvature: a variational approach. Memoirs of the American Mathematical Society, 2019, 256 (1225), ⟨10.1090/memo/1225⟩. ⟨hal-00838195⟩
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