on the characteristic of projectively invariant pseudo-distance on finsler spaces

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler space. moreover, the ricci tensor is used to define a finsler structure and it is shown that, the pseudo-distance is trivial on complete finsler spaces of positive semi-definite ricci tensor and it is a distance on a finsler space of parallel negative definite ricci tensor.