On the characteristic of projectively invariant Pseudo-distance on Finsler spaces

Abstract

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.