  This article is an exposition of four loosely related remarks on the geometry
of Finsler manifolds with constant positive flag curvature.
  <p> The first remark is that there is a canonical Kahler structure on the
space of geodesics of such a manifold.
  <p> The second remark is that there is a natural way to construct a (not
necessarily complete) Finsler n-manifold of constant positive flag curvature
out of a hypersurface in suitably general position in complex projective
n-space.
  <p> The third remark is that there is a description of the Finsler metrics of
constant curvature on the 2-sphere in terms of a Riemannian metric and 1-form
on the space of its geodesics. In particular, this allows one to use any
(Riemannian) Zoll metric of positive Gauss curvature on the 2-sphere to
construct a global Finsler metric of constant positive curvature on the
2-sphere.
  <p> The fourth remark concerns the generality of the space of (local) Finsler
metrics of constant positive flag curvature in dimension n+1>2 . It is shown
that such metrics depend on n(n+1) arbitrary functions of n+1 variables and
that such metrics naturally correspond to certain torsion-free S^1 x
GL(n,R)-structures on 2n-manifolds. As a by-product, it is found that these
groups do occur as the holonomy of torsion-free affine connections in dimension
2n, a hitherto unsuspected phenomenon.
