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(Ebook) Curvature: a Variational Approach by A. Agrachev; D. Barilari; L. Rizzi ISBN 9781470449131, 1470449137

  • SKU: EBN-51644612
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Authors:A. Agrachev; D. Barilari; L. Rizzi
Pages:154 pages.
Year:2019
Editon:1
Publisher:American Mathematical Society
Language:english
File Size:3.24 MB
Format:pdf
ISBNS:9781470449131, 1470449137
Categories: Ebooks

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(Ebook) Curvature: a Variational Approach by A. Agrachev; D. Barilari; L. Rizzi ISBN 9781470449131, 1470449137

The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot-Carathéodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.
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