A note on the Lorentzian splitting theorem
Differential Geometry
2025-04-22 v2 General Relativity and Quantum Cosmology
Abstract
We present a version of the Lorentzian splitting theorem under a weakened Ricci curvature condition. The proof makes use of basic properties of achronal limits [19], [20], together with the geometric maximum principle for spacelike hypersurfaces in [1]. Our version strengthens a related result in [29] in the globally hyperbolic setting by removing a certain boundedness condition on the Ricci curvature.
Cite
@article{arxiv.2504.05028,
title = {A note on the Lorentzian splitting theorem},
author = {Gregory J. Galloway},
journal= {arXiv preprint arXiv:2504.05028},
year = {2025}
}
Comments
12 pages; v2: a pertinent reference, and some related comments, added. Title and abstract also modified