# On m-th root Finsler metrics

## TL;DR

This paper characterizes specific properties of m-th root Finsler metrics, showing that under certain curvature conditions, these metrics simplify to weakly Berwald metrics, advancing understanding in Finsler geometry.

## Contribution

It provides a characterization of locally dually flat and Antonelli m-th root Finsler metrics and shows their reduction to weakly Berwald metrics under isotropic mean Berwald curvature.

## Key findings

- Characterization of locally dually flat m-th root Finsler metrics
- Characterization of Antonelli m-th root Finsler metrics
- Reduction of isotropic mean Berwald curvature m-th root metrics to weakly Berwald metrics

## Abstract

In this paper, we characterize locally dually flat and Antonelli $m$-th root Finsler metrics. Then, we show that every $m$-th root Finsler metric of isotropic mean Berwald curvature reduces to a weakly Berwald metric.