Matsumoto metrics of constant flag curvature are trivial
  The local structure of Finsler metrics of constant flag curvature have been historically mysterious. It is proved that every Matsumoto metric of constant flag curvature on a manifold of dimension n \geq 3 is either Riemannian or locally Minkowskian. 
M. Rafie-Rad, B. Rezaei
math.DG math-ph math.MP