On dually flat $(\alpha,\beta)$-metrics

TL;DR

This paper introduces a novel method using $eta$-deformations to analyze the dual flatness of $( ext{alpha},eta)$-metrics in Finsler geometry, extending previous work on Randers metrics.

Contribution

The paper presents a new approach employing $eta$-deformations to study dual flatness in $( ext{alpha},eta)$-metrics, advancing the understanding of Finsler geometric structures.

Findings

$eta$-deformations effectively analyze dual flatness.

Extension of dual flat Randers metrics to broader $( ext{alpha},eta)$-metrics.

New techniques in Finsler geometry for metric deformation analysis.

Abstract

In this paper, I will show how to use $\beta$-deformations to deal with dual flatness of $(\alpha,\beta)$-metrics. It is a natural continuation of the research on dually flat Randers metrics(see arxiv:1209.1150). $\beta$-deformations is a new method in Riemann-Finsler geometry, it is introduced by the author(see arxiv:1209.0845).