# On m-th root metrics with special curvature properties

## TL;DR

This paper proves that m-th root Finsler metrics with certain curvature properties simplify to more specific types, revealing their geometric structure and curvature behavior.

## Contribution

It demonstrates that m-th root Finsler metrics with isotropic Landsberg curvature are actually Landsberg metrics and those with almost vanishing H-curvature have vanishing H-curvature.

## Key findings

- m-th root Finsler metrics with isotropic Landsberg curvature reduce to Landsberg metrics
- m-th root metrics with almost vanishing H-curvature have vanishing H-curvature
- clarifies curvature properties of m-th root Finsler metrics

## Abstract

In this Note, we prove that every m-th root Finsler metric with isotropic Landsberg curvature reduces to a Landsberg metric. Then, we show that every m-th root metric with almost vanishing H-curvature has vanishing H-curvature.