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arXiv · 1306.5318

Curvature: a variational approach

Andrei Agrachev·Davide Barilari·Luca Rizzi
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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.

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Andrei Agrachev, Davide Barilari, Luca Rizzi. 2013-06-22. Curvature: a variational approach. https://doi.org/10.1090/memo/1225

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