The $m$-th root Finsler metrics admitting $(\alpha,\beta)$-types
Bull. Korean Math. Soc. 2004 Vol. 41, No. 1, 45-52 Printed 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 , and applied to the biology  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.