Finsleroid-regular space developed. Berwald case

TL;DR

This paper develops the Finsleroid-regular space within the Berwald class, deriving explicit spray coefficients and exploring its extension into pseudo-Finsleroid domains, under specific assumptions about the 1-form and charge.

Contribution

It introduces the Finsleroid-regular Berwald space, providing explicit formulas for spray coefficients and conditions for regularity and extension.

Findings

Derived explicit spray coefficients for Finsleroid-regular space.

Identified conditions for the space to be a Berwald space.

Extended the regular Finsleroid space into pseudo-Finsleroid domain.

Abstract

The Finsleroid--Finsler space becomes regular when the norm $||b||=c$ of the input 1-form $b$ is taken to be an arbitrary positive scalar $c(x) < 1$. By performing required direct evaluations, the respective spray coefficients have been obtained in a simple and transparent form. The adequate continuation into the regular pseudo-Finsleroid domain has been indicated. The Finsleroid-regular Berwald space is found under the assumptions that the Finsleroid charge is a constant and the 1-form $b$ is parallel. Keywords: Finsler metrics, spray coefficients, curvature tensors.