J. Korean Math. Soc.
Online first article October 20, 2023
Copyright © The Korean Mathematical Society.
Salah Gomaa Elgendi and Amr Soleiman
Associate Professor - Faculty of Science - Benha University, Professor - Faculty of Science - Benha University
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.
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