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 The $m$-th root Finsler metrics admitting $(\alpha,\beta)$-types Bull. Korean Math. Soc. 2004 Vol. 41, No. 1, 45-52 Published online March 1, 2004 Byung-Doo Kim and Ha-Yong Park Kyungil University, Kyungil University Abstract : The theory of $m$-th root metric has been developed by H. Shimada [8], and applied to the biology [1] as an ecological metric. The purpose of this paper is to introduce the $m$-th root Finsler metrics which admit $(\alpha,\beta)$-types. Especially in cases of $m=3, 4$, we give the condition for Finsler spaces with such metrics to be locally Minkowski spaces. Keywords : Berwald space, locally Minkowski, $m$-th root metric MSC numbers : 53B40 Downloads: Full-text PDF