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An intrinsic proof of Numata's theorem on Landsberg spaces

Author name : AMR SOLIMAN MAHMOUD HASSAN
Publication Date : 2023-10-20
Journal Name : J. Korean Math. Soc.

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.

Publication Link

https://doi.org/10.4134/JKMS.j230263

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