On spherically symmetric Finsler metric with scalar and constant flag curvature

Abstract

In this paper we study spherically symmetric metrics on a symmetric space in Rn 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 locally projectively flat Finsler metrics are given. We also provide a family of spherically symmetric Finsler metrics which are not of Douglas type.