Curvature: A Variational Approach (Memoirs of the American Mathematical Society) - Softcover

Agrachev, A.; Barilari, D.; Rizzi, L.

Softcover

ISBN 10: 1470426463 ISBN 13: 9781470426460

Publisher: Amer Mathematical Society, 2018

Synopsis

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-Caratheodory) 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.

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 2018
• ISBN 10: 1470426463
• ISBN 13: 9781470426460
• Binding: Paperback
• Language: English
• Number of pages: 116