Finsleroid-regular space. Landsberg-to-Berwald implication

TL;DR

This paper demonstrates that in Finsleroid-regular spaces, the Landsberg condition simplifies to the Berwald condition across all dimensions, providing clear representations and comparisons with Finsleroid-Finsler spaces.

Contribution

It establishes that the Landsberg-to-Berwald implication holds in Finsleroid-regular spaces, clarifying their geometric structure and relations.

Findings

Landsberg condition degenerates to Berwald condition in Finsleroid-regular spaces

Provides explicit expository representations of these spaces

Includes comparisons with Finsleroid-Finsler spaces

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 $N\ge2$). Simple and clear expository representations are obtained. Due comparisons with the Finsleroid-Finsler space are indicated. Keywords: Finsler metrics, spray coefficients, curvature tensors.