Kropina change of a Finsler space with m-th root metric

TL;DR

This paper investigates conditions under which a Finsler space with a Kropina change of an m-th root metric relates projectively to the original and explores when it is locally dually flat or projectively flat.

Contribution

It provides new conditions for projective relatedness, dual flatness, and projective flatness of Kropina changed m-th root Finsler metrics.

Findings

Conditions for projective relatedness to m-th root metric

Criteria for local dual flatness of the transformed metric

Conditions for projective flatness of the Kropina changed metric

Abstract

In this paper, we find a condition under which a Finsler space with Kropina change of mth-root metric is projectively related to a mth-root metric and also we find a condition under which this Kropina transformed mth-root metric is locally dually flat. Moreover we find the condition for its Projective flatness.