On a classification of fat bundles over compact homogeneous spaces
  This article deals with fat bundles. Berard-Bergery classified all homogeneous bundles of that type. We ask a question of a possibility to generalize his description in the case of arbitrary G-structures over homogeneous spaces. We obtain necessary conditions for the existence of such bundles. These conditions yield a kind of classification of fat bundles associated with G-structures over compact homogeneous spaces provided that the connection in a G-structure is canonical. 
Maciej Bochenski, Anna Szczepkowska, Aleksy Tralle, Artur Woike
math.DG