On the flag curvature of a homogeneous Finsler sapce with generalized $m$-Kropina metric

TL;DR

This paper derives an explicit formula for the flag curvature of homogeneous Finsler spaces with generalized m-Kropina metrics, explores the equivalence of reductive conditions, and studies curvature properties in naturally reductive cases.

Contribution

It provides a new explicit formula for flag curvature and establishes the equivalence of two definitions of naturally reductive spaces for generalized m-Kropina metrics.

Findings

Explicit formula for flag curvature derived

Equivalence of reductive definitions shown under mild conditions

Flag curvature properties studied in naturally reductive spaces

Abstract

In this paper, first, we give an explicit formula for the flag curvature of a homogeneous Finsler space with generalized $m$-Kropina metric. Then, we show that, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space are equivalent for afore said metric. Finally, we study the flag curvature of naturally reductive homogeneous Finsler spaces with generalized $m$-Kropina metric.