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 locally projectively flat Finsler metrics are given. We also provide a family of spherically symmetric Finsler metrics which are not of Douglas type.

中文翻译：

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关于具有标量和恒定旗曲率的球对称 Finsler 度量

在本文中，我们研究了对称空间上的球对称度量 ${\mathbb{电阻}}^n$具有标量和恒定标志曲率，我们还获得了此类指标的系列。为具有标量和恒定标志曲率的道格拉斯度量提供了许多明确的示例。此外，还给出了局部投影平坦 Finsler 度量的新示例。我们还提供了一系列非 Douglas 类型的球对称 Finsler 度量。