Methods of Riemannian geometry in the Finsler geometry

我们的目标是解决Finlser几何中的以下三个问题：问题1(Landsberg Unicorn问题)。证明或反驳下面的猜想：Landsberg曲率的消失意味着度量是Berwald。问题2.描述包含二维和三维伪射影变换群的二维Finlser度量。问题3.证明或反驳以下猜想：在负Euler特征的闭曲面上，两个射影等价的Finsler度量在平凡投射上等价。

Our goal is to solve the following three problems in Finlser geometry:Problem 1 (Landsberg Unicorn Problem). Prove or disprove the following conjecture: Vanishing of the Landsberg curvature implies that the metric is Berwald.Problem 2. Describe 2-dimensional Finlser metrics admitting 2- and 3- dimensional pseudogroup of projective transformations.Problem 3. Prove or disprove the following conjecture: on a closed surface of negative Euler characteristic two projectively equivalent Finsler metrics are trivially projectively equivalent.