Non-existence of Funk functions for Finsler spaces of non-vanishing   scalar flag curvature
  In his book "Differential Geometry of Spray and Finsler spaces", page 177, Zhongmin Shen asks "wether or not there always exist non-trivial Funk functions on a spray space". In this note, we will prove that the answer is negative for the geodesic spray of a finslerian function of non-vanishing scalar flag curvature. 
Ioan Bucataru, Zolt\'an Muzsnay
math.DG