Four-dimensional Conformally Flat Berwald and Landsberg Spaces

TL;DR

This paper investigates conditions under which four-dimensional conformally flat Landsberg Finsler spaces become Berwald spaces, extending previous three-dimensional studies and contributing to the understanding of conformal transformations in higher-dimensional Finsler geometry.

Contribution

It extends the study of conformal flatness from three to four dimensions and identifies conditions for Landsberg spaces to be Berwald spaces.

Findings

Derived conditions for conformally flat Landsberg spaces to be Berwald spaces.

Extended conformal flatness analysis to four-dimensional Finsler spaces.

Contributed to the classification of Finsler spaces under conformal transformations.

Abstract

The problem of conformal transformation and conformal flatness of Finsler spaces has been studied by so many researchers $\left[ 6,16,17,20,21\right] .$ Recently, Prasad et. al $\left[ 19\right] $ have studied three dimensional conformally flat Landsberg and Berwald spaces and have given some important results. The purpose of the present paper is to extend the idea of conformal change to four dimensional Finsler spaces and find the suitable conditions under which a four dimensional conformally flat Landsberg space becomes a Berwald space.