Submetries in non-positive signature and applications

Matteo Zanardini

Submetries in non-positive signature and applications

Differential Geometry 2026-07-14 v1

Authors: Matteo Zanardini

Abstract

We consider a generalization of the notion of submetry tailored to the setting of spacetimes. We show that, under suitable completeness assumptions, Lorentzian submetries between smooth spacetimes correspond to locally C^{1,1} Semi-Riemannian submersions. Moreover, we establish some applications regarding timelike curvature bounds, isometric group actions, acausal foliations and Lorentz-Wasserstein geometry.

Keywords

submetry Lorentzian submetry semi-Riemannian submersion timelike curvature bounds isometric group actions acausal foliations Lorentz-Wasserstein geometry

Cite

@article{arxiv.2607.12516,
  title  = {Submetries in non-positive signature and applications},
  author = {Matteo Zanardini},
  journal= {arXiv preprint arXiv:2607.12516},
  year   = {2026}
}

Comments

25 pages, 2 figures