What are some open problems in subRiemannian geometry?
I am interested especially in problems concerning connections and curvature, but any contribution is welcomed.
What are some open problems in subRiemannian geometry? I am interested especially in problems concerning connections and curvature, but any contribution is welcomed. 


Chapter 10 of "A Tour of Subriemannian Geometries, Their Geodesics and Applications" describes four open problems. 


Finding subriemannian geodesics of homogeneous spaces is one problem of practical importance. See http://hrl.harvard.edu/publications/khaneja02subriemannian.pdf 


Andrei Agrachev recently posted an article on the arXiv: http://arxiv.org/abs/1304.2590 entitled "Some open problems" that you might find interesting. He discusses several open problems in control theory and subRiemannian geometry that are of considerable interest. 

