On cylindrical symmetric projectively flat Finsler metrics

TL;DR

This paper investigates cylindrical symmetric Finsler metrics that are projectively flat, deriving differential equations, providing solutions, and including examples to illustrate the properties of such metrics.

Contribution

It introduces a system of differential equations characterizing projectively flat cylindrical symmetric Finsler metrics and offers explicit solutions and examples.

Findings

Derived differential equations for projectively flat cylindrical symmetric Finsler metrics

Provided explicit solutions and examples illustrating these metrics

Enhanced understanding of the structure of such Finsler metrics

Abstract

We study the cylindrical symmetric Finsler metrics. We obtain the system of differential equations of such metrics which are projectively flat. We give a family of solutions of this system. Examples are included.