  We give a simple characterization of the parabolic geodesics introduced by
Cap, Slovak and Zadnik for all parabolic geometries. This goes through the
definition of a natural connection on the space of Weyl structures. We then
show that parabolic geodesics can be characterized as the following data: a
curve on the manifold and a Weyl structure along the curve, so that the curve
is a geodesic for its companion Weyl structure and the Weyl structure is
parallel along the curve and in the direction of the tangent vector of the
curve.
