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

Document Type: Regular Paper

Authors

Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave., 15914 Tehran, Iran

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.

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