Journal of the
Korean Mathematical Society JKMS

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 ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature

Keywords: Berwald manifold; Landsberg manifold; C-reducible; scalar curvature.

MSC numbers: 53C60, 53B40, 58B20.