English

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 n3n\geq 3 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}
}

Comments

11 pages