THE m-TH ROOT FINSLER METRICS ADMITTING (α, β)-TYPES

Abstract

THE m-TH ROOT FINSLER METRICS ADMITTING (α, β)-TYPES Berwald space;locally Minkowski;m-th root metric; 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.