Kropina metrics and Zermelo navigation on Riemannian manifolds
  The present paper studies globally defined Kropina metrics as solutions of the Zermelo's navigation problem. Moreover, we characterize the Kropina metrics of constant flag curvature showing that up to local isometry, there are only two model spaces of them: the Euclidean space and the odd-dimensional spheres. 
Ryozo Yoshikawa and Sorin V. Sabau
math.DG