In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, a 1-form, and its norm and find equations with sufficient conditions for such Finsler metrics to become Ricci-flat. Using certain transformations, we show that these equations have solutions and lead to the construction of a large and special class of Einstein metrics.

中文翻译：

---

关于爱因斯坦芬斯勒指标

在本文中，我们研究了用黎曼度量、1-形式及其范数表示的 Finsler 度量，并找到了具有足够条件使这些 Finsler 度量成为 Ricci-flat 的方程。使用某些变换，我们证明这些方程有解，并导致构建大量特殊的爱因斯坦度量。