In this paper, we investigate the flag curvature of a special class of Finsler metrics called general spherically symmetric Finsler metrics, which are defined by a Euclidean metric and two related 1-forms. We find equations to characterize the class of metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover, we study general spherically symmetric Finsler metrics with the vanishing non-Riemannian quantity χ-curvature. In particular, we construct some new projectively flat Finsler metrics of constant flag curvature.

中文翻译：

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具有恒定Ricci和标志曲率的通用球对称Finsler度量

在本文中，我们研究了称为通用球对称Finsler度量的一类特殊Finsler度量的旗曲率，该度量由欧几里德度量和两个相关的1形式定义。我们找到方程来表征具有恒定Ricci曲率（张量）和恒定标志曲率的度量标准类别。此外，我们研究了具有消失的非黎曼量χ曲率的一般球对称Finsler度量。特别是，我们构造了一些恒定的旗面曲率的新的投影平坦Finsler度量。