CarnotCarathéodoryMetrik
The Carnot-Carathéodory metric, also known as the sub-Riemannian metric or Hörmander metric, is a concept in differential geometry that generalizes the standard Riemannian metric. It is defined on a manifold equipped with a distribution, which is a subbundle of the tangent bundle. Instead of considering curves whose tangent vectors lie in the entire tangent space, the Carnot-Carathéodory metric restricts tangent vectors to lie within the specified distribution.
The distance between two points in this metric is defined as the infimum of the lengths of
A key property of the Carnot-Carathéodory metric is that it satisfies the Carathéodory-Carathéodory condition, which ensures