Some elementary observations regarding reductive Cartan geometries
  After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary results from Riemannian geometry are proven using these generalizations. In particular, a generalization of the Hopf-Rinow theorem is given with a pleasantly concise proof. 
Jacob W. Erickson
math.DG