Lorentz meets Ptolemy
Differential Geometry
2026-01-30 v1 Metric Geometry
Abstract
We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curvature bound from above by zero. We investigate the link between the Ptolemy inequality and the hyperbolic inversion and establish some applications and rigidity properties.
Cite
@article{arxiv.2601.21596,
title = {Lorentz meets Ptolemy},
author = {Felix Rott and Zhe-Feng Xu and Matteo Zanardini},
journal= {arXiv preprint arXiv:2601.21596},
year = {2026}
}
Comments
20 pages, 3 Figures