  We show that which that for a Berwald structure, any Riemannian structure
that is preserved by the Berwald connection leaves the indicatrix invariant
under horizontal parallel transport. We also obtain the converse result: if
$({\bf M},F)$ is a Finsler structure such that there exists a Riemannian
structure that leaves invariant the indicatrix under parallel transport of the
associated Levi-Civita connection, then the structure $({\bf M},F)$ is Berwald.
As application, a necessary condition for pure Landsberg spaces is formulated.
Using this criterion we provide an strategy to solve the existence or not of
pure Landsberg surfaces
