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 ≥ 3 of non-zero scalar
curvature are Riemannian spaces of constant curvature
Keywords
Berwald manifold, Landsberg manifold, C-reducible, scalar curvature.