Curvature: A Variational Approach - Brossura

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

Brossura

ISBN 10: 1470426463 ISBN 13: 9781470426460

Casa editrice: Amer Mathematical Society, 2019

Riassunto

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.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2019
• Lingua: Inglese
• ISBN 10: 1470426463
• ISBN 13: 9781470426460
• Rilegatura: Copertina flessibile
• Numero di pagine: 116
• Contatto del produttore: non disponibile