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On the characteristic of projectively invariant Pseudo-distance on Finsler spaces | ||
| Iranian Journal of Science | ||
| مقاله 13، دوره 39، شماره 2، شهریور 2015، صفحه 233-238 اصل مقاله (303.92 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2015.3023 | ||
| نویسندگان | ||
| B. Bidabad* ؛ M. Sepasi | ||
| Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave., 15914 Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Finsler metric؛ Schwarzian derivative؛ Ricci tensor؛ projective parameter؛ pseudo-distance | ||
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