Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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AN INTRINSIC PROOF OF NUMATA'S THEOREM ON LANDSBERG SPACES

  • Salah Gomaa Elgendi (Department of Mathematics Faculty of Science Islamic University of Madinah, Department of Mathematics Faculty of Science Benha University) ;
  • Amr Soleiman (Department of Mathematics College of Science and Arts - Qurayyat Al Jouf University, Department of Mathematics Faculty of Science Benha University)
  • Received : 2023.05.19
  • Accepted : 2023.09.12
  • Published : 2024.01.01
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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.

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References

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