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On a class of projectively flat (α,β) metrics | ||
| Journal of Finsler Geometry and its Applications | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 اردیبهشت 1405 اصل مقاله (287.36 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2026.18452.1187 | ||
| نویسندگان | ||
| Mehdi Tavakkoli1؛ Mehdi Rafie-Rad* 2 | ||
| 1Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| چکیده | ||
| Given any Finsler metric F on a smooth manifold, its symmetrized metric Fˆ(x,y):=1/2(F(x,y)+F(x,-y) may inherit some geometric properties of F. We examine this fact for the Matsumoto metric F=α2/(α-β) and prove that if the Matsumoto metric is locally projectively flat then, so is its symmetrized metric Fˆ=α3/(α2-β2). In particular, the converse result also holds. | ||
| کلیدواژهها | ||
| Finsler metric؛ (α,β)-metrics؛ Matsumoto metric؛ symmetrized metrics | ||
| مراجع | ||
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