MathDBLandsberg's unicorn conjecture
Landsberg's unicorn conjecture
Let be a Finsler metric, and let its Landsberg curvature be the corresponding non-Riemannian curvature tensor. A Finsler metric is Berwald when its Berwald parallel transport is linear; a non-Berwald Finsler metric with vanishing Landsberg curvature is called a unicorn metric. Landsberg's unicorn conjecture. A Finsler metric with vanishing Landsberg curvature must be Berwald. Smooth unicorn metrics are believed not to exist, making this one of the main open problems in Finsler geometry; the conjecture remains open in general.
Sources & referencesView supporting material
Primary source
Ming Xu and Vladimir S. Matveev, “Proof of Laugwitz Conjecture and Landsberg Unicorn Conjecture for Minkowski norms with SO(k)SO(n-k)-symmetry”, arXiv:2007.15888 (2020).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.