  Locally projectively flat metrics (or sprays) form a rich class of metrics
(or sprays) in Finsler and spray geometry. The characterization of such metrics
is the Hilbert Fourth Problem in the regular case. In this paper we study the
Pontrjagin classes of a manifold given a spray structure, and show that a
manifold equipped with a locally projectively flat Finsler metric (or spray)
has zero Pontrjagin classes.
