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J. Korean Math. Soc. 2024; 61(1): 149-160
Online first article October 20, 2023 Printed January 1, 2024
https://doi.org/10.4134/JKMS.j230263
Copyright © The Korean Mathematical Society.
An intrinsic proof of Numata's theorem on Landsberg spaces
Salah Gomaa Elgendi, Amr Soleiman
Benha University; 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 $n\geq 3$ of non-zero scalar curvature are Riemannian spaces of constant curvature.
Keywords: Berwald manifold, Landsberg manifold, $C$-reducible, scalar curvature
MSC numbers: Primary 53C60, 53B40, 58B20
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