On 5-manifolds admitting rank two distributions of Cartan type
  We consider the question whether an orientable 5-manifold can be equipped with a rank two distribution of Cartan type and what 2-plane bundles can be realized. We obtain a complete answer for open manifolds. In the closed case, we settle the topological part of this problem and present partial results concerning its geometric aspects and new examples. 
Shantanu Dave and Stefan Haller
math.DG math.KT