Methods of Riemannian geometry in the Finsler geometry

• Applicant: Professor Dr. Vladimir Matveev
• Subject Area: Mathematics
• Term: from 2016 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 318916629

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.

• DFG Programme: Research Grants