On cylindrical symmetric Finsler metrics with vanishing Douglas curvature

TL;DR

This paper investigates cylindrically symmetric Finsler metrics, deriving their Douglas curvature and the differential equations characterizing those with zero Douglas curvature, supported by multiple examples.

Contribution

It provides explicit formulas for Douglas curvature and characterizes cylindrically symmetric Finsler metrics with vanishing Douglas curvature through differential equations.

Findings

Explicit formulas for Douglas curvature of cylindrically symmetric Finsler metrics

Differential equations for metrics with zero Douglas curvature

Multiple illustrative examples included

Abstract

In this paper, we consider the cylindrically symmetric Finsler metrics and we obtain their Douglas curvature. Furthermore, we obtain the differential equation system of the cylindrically symmetric Finsler metrics with vanishing Douglas curvature. Many examples are included.