An intrinsic proof of Numata's theorem on Landsberg spaces
Differential Geometry
2023-04-18 v1
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 of non-zero scalar curvature are Riemannian spaces of constant curvature.
Keywords
Cite
@article{arxiv.2304.07925,
title = {An intrinsic proof of Numata's theorem on Landsberg spaces},
author = {Amr Soleiman and Salah G. Elgendi},
journal= {arXiv preprint arXiv:2304.07925},
year = {2023}
}
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11 pages