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.
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Curvature: a variational approach. Memoirs of the American Mathematical Society; Bd. volume 256, number 1225 (first of 6 numbers).
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Providence, American Mathematical Society, 2018
ISBN 10: 1470426463
ISBN 13: 9781470426460
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Softcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03297 9781470426460 Sprache: Englisch Gewicht in Gramm: 550. Seller Inventory # 2489203
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