On spherically symmetric Finsler metric with scalar and constant flag curvature

TL;DR

This paper investigates spherically symmetric Finsler metrics with scalar and constant flag curvature, providing explicit examples, including projectively flat metrics and non-Douglas types, expanding the understanding of such geometries.

Contribution

It introduces new families of spherically symmetric Finsler metrics with scalar and constant flag curvature, including explicit examples and non-Douglas types.

Findings

Explicit examples of Douglas metrics with constant flag curvature

New projectively flat Finsler metrics

Family of spherically symmetric metrics not of Douglas type

Abstract

In this paper we study spherically symmetric metrics on a symmetric space in $\mathbb{R}^n$ with scalar and constant flag curvature and we also obtain families of this type of metrics. Many explicit examples are provided for Douglas metrics with scalar and constant flag curvature. Furthermore, new examples of projectively flat Finsler metrics are given. We also provide a family of spherically symmetric Finsler metrics which are not of Douglas type.