Curvature A Variational Approach

Van Leeuwen, Anne M.

ISBN 10: 1470426463 / ISBN 13: 9781470426460

Editore: Amer Mathematical Society, 2018

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Dati bibliografici

• Titolo: Curvature A Variational Approach
• Editore: Amer Mathematical Society
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 1470426463
• ISBN 13: 9781470426460
• Rilegatura: Brossura
• Condizione: New

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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.