Hurewicz fibrations, almost submetries and critical points of smooth   maps
  We prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric properties of maps between compact Riemannian manifolds under curvature restrictions. 
S.L. Cacciatori and S. Pigola
math.AT