Methods of Riemannian geometry in the Finsler geometry

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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.