# General $(\alpha, \beta)$ metrics with relatively isotroic mean Landsberg curvature

## TL;DR

This paper investigates a new class of Finsler metrics called general (,) metrics, establishing conditions under which metrics with relatively isotropic mean Landsberg curvature are Berwald, thus advancing understanding of Finsler geometry.

## Contribution

It provides a necessary and sufficient condition for general (,) metrics with isotropic mean Landsberg curvature to be Berwald, under specific assumptions.

## Key findings

- Derived a condition linking isotropic mean Landsberg curvature to Berwald metrics.
- Extended the understanding of (,) Finsler metrics with conformal 1-forms.
- Identified criteria for when these metrics exhibit Berwald properties.

## Abstract

In this paper, we study a new class of Finsler metrics, F=\alpha\phi(b^2,s), s:=\beta/\alpha, defined by a Riemannian metric \alpha and 1-form \beta. It is called general (\alpha, \beta) metric. In this paper, we assume \phi be coefficient by s and \beta be closed and conformal. We find a nessecary and sufficient condition for the metric of relatively isotropic mean Landsberg curvature to be Berwald.