There exist no locally symmetric Finsler spaces of positive or negative   flag curvature
  We show that the results of Foulon (1997 an 2002) and Kim (2007) (independently, Deng and Hou (2007)) about the nonexistence of locally symmetric Finsler metrics of positive or negative flag curvature are in fact local. 
Vladimir S. Matveev
math.DG