An intrinsic proof of Numata's theorem on Landsberg spaces

Abstract

In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension $n\geq 3$ of non-zero scalar curvature are Riemannian spaces of constant curvature.