The curvature: a variational approach

摘要: The curvature discussed in this paper is a far reaching generalisation of the Riemannian sectional curvature. We give unified definition which applies to wide class geometric structures whose geodesics arise from optimal control problems, including Riemannian, subRiemannian, Finsler and sub-Finsler spaces. Special attention paid sub-Riemannian (or Carnot–Caratheodory) metric Our construction direct naive, similar original approach Riemann. In particular, we extract invariants asymptotics cost problems. Surprisingly, it works very general setting and, for all