2014/04/14 by Xu, Ming, Deng, Shaoqiang
#22E46 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1404.3488
Given a Finsler space, we introduce a system of partial differential equations, called the Landsberg equation. Based on a careful analysis of the Landsberg equation and the observation that the solution space is invariant under the linear isometries of the tangent Minkowski spaces, we prove that an (α1, α2)-metric of the Landsberg type must be a Berwald metric. This shows that the hunting for a unicorn, one of the longest standing open problem in Finsler geometry, cannot be successful even in the very broad class of (α1,α2)-metrics.