In this paper, we prove two rigidity results for non-positively curved homogeneous Finsler metrics. Our first main result yields an extension of Hu-Deng's well-known result proven for the Randers metrics. Indeed, we prove that every connected homogeneous Finsler space with non-positive flag curvature and isotropic S-curvature is Riemannian or locally Minkowskian. We extend the Szabó's rigidity theorem for Berwald surfaces and show that homogeneous isotropic Berwald metrics with non-positive flag curvature are Riemannian or locally Minkowskian. Our second main result is to show that every homogeneous $(\alpha ,\beta )$-metric with non-positive flag curvature and almost isotropic S-curvature is Riemannian or locally Minkowskian.

在本文中，我们证明了非正弯曲齐次 Finsler 度量的两个刚性结果。我们的第一个主要结果产生了 Hu-Deng 著名结果的扩展，该结果已为 Randers 指标证明。事实上，我们证明了每个具有非正旗曲率和各向同性 S 曲率的连通齐次 Finsler 空间都是黎曼或局部闵可夫斯基空间。我们扩展了 Berwald 曲面的 Szabó 刚性定理，并表明具有非正旗曲率的齐次各向同性 Berwald 度量是黎曼或局部闵可夫斯基。我们的第二个主要结果是证明每个同质的$(\alpha ,\beta )$-具有非正标志曲率和几乎各向同性 S 曲率的度量是黎曼或局部闵可夫斯基。