论文标题
完整的Finsler歧管的一些刚性结果
Some Rigidity Results on Complete Finsler Manifolds
论文作者
论文摘要
我们提供了Obata定理的扩展，以基于二阶微分方程来建立一些刚性结果。主要是，我们证明，正恒定标志曲率的每个完整连接的Finsler歧管在具有某些Finsler Metric的欧几里得球体上是同构的同型，反之亦然。基于这些结果，我们提出了芬斯勒歧管的分类，该分类允许跨正常功能。具体而言，我们表明，如果完整的鳍歧管允许具有两个关键点的跨正常函数，那么它对球体是同构的。
We provide an extension of Obata's theorem to Finsler geometry and establish some rigidity results based on a second order differential equation. Mainly, we prove that every complete connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to an Euclidean sphere endowed with a certain Finsler metric and vice versa. Based on these results, we present a classification of Finsler manifolds which admit a transnormal function. Specifically, we show that if a complete Finsler manifold admits a transnormal function with exactly two critical points, then it is homeomorphic to a sphere.
