Every Finsler metric induces a spray on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called the projective Ricci curvature. The projective Ricci curvature is an important projective invariant in Finsler geometry. In this paper, we study and characterize projectively Ricci-flat square metrics. Moreover, we construct some nontrivial examples on such Finsler metrics.

中文翻译：

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关于一类射影Ricci-flat Finsler度量

每个Finsler指标都会在歧管上产生喷雾。通过歧管上的容积形式，每个喷雾都可以变形为投射喷雾。投射喷雾的Ricci曲率称为投射Ricci曲率。Ricci射影曲率是Finsler几何中重要的射影不变量。在本文中，我们研究并刻画了Ricci-flat平方度量。此外，我们在这样的Finsler指标上构造了一些非平凡的例子。