Finsleroid-regular space. Landsberg-to-Berwald implication

Abstract

By performing required evaluations, we show that in the Finsleroid-regular space the Landsberg-space condition just degenerates to the Berwald-space condition (at any dimension number $N\ge 2$). Simple and clear expository representations are obtained. Due comparisons with the Finsleroid-Finsler space are indicated. Keywords: Finsler metrics, spray coefficients, curvature tensors.