Spherically symmetric Finsler metrics satisfying the $σ$T-condition

Salah G. Elgendi

Spherically symmetric Finsler metrics satisfying the $σ$T-condition

Differential Geometry 2026-07-09 v1

Authors: Salah G. Elgendi

Abstract

In this paper, we present a complete characterization of spherically symmetric Finsler metrics that satisfy the $\sigma T$ -condition. We further investigate the subclass of such metrics within the Landsberg category and identify the precise conditions under which spherically symmetric Finsler metrics satisfying the $T$ -condition must also be Berwaldian. In addition, we construct new non-regular solutions to the classical unicorn problem, providing explicit examples of Landsberg metrics that are not Berwaldian.

Keywords

Finsler metrics spherically symmetric T-condition Landsberg metrics Berwald metrics unicorn problem

Cite

@article{arxiv.2607.08217,
  title  = {Spherically symmetric Finsler metrics satisfying the $σ$T-condition},
  author = {Salah G. Elgendi},
  journal= {arXiv preprint arXiv:2607.08217},
  year   = {2026}
}

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14 pages