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.
€118.71
यह ईबुक खरीदें और 1 और मुफ़्त पाएं!
स्वरूप PDF ● पेज 142 ● ISBN 9781470449131 ● प्रकाशक American Mathematical Society ● प्रकाशित 2019 ● डाउनलोड करने योग्य 3 बार ● मुद्रा EUR ● आईडी 8057314 ● कॉपी सुरक्षा Adobe DRM
एक DRM सक्षम ईबुक रीडर की आवश्यकता है
एक ही लेखक से अधिक ईबुक / संपादक
48,763 इस श्रेणी में ईबुक
