Transverse Geometry of Lorentzian foliations with applications to Lorentzian orbifolds

[2402.05907] Transverse Geometry of Lorentzian foliations with applications to Lorentzian orbifolds Skip to main content Search Submit Donate Log in Mathematics > Differential Geometry arXiv:2402.05907 (math) [Submitted on 8 Feb 2024 ( v1 ), last revised 24 Aug 2026 (this version, v2)] Title: Transverse Geometry of Lorentzian foliations with applications to Lorentzian orbifolds Authors: Francisco C. Caramello Jr , Henrique A. Puel Martins , Ivan P. Costa e Silva View PDF HTML (experimental) Abstract: We prove a transverse diameter theorem in the context of Lorentzian foliations, which can be interpreted as a Hawking--Penrose-type singularity theorem for timelike geodesics transverse to the foliation. In order to develop the necessary machinery we introduce and study a novel causality structure on the leaf space via the transverse Lorentzian geometry on the foliated manifold. We describe the initial rungs of a transverse causal ladder and relate them to their standard counterparts on an underlying foliated spacetime. We show how these results can be interpreted as doing Lorentzian (and more generally semi-Riemannian) geometry on low-regularity spaces that can be realized as leaf spaces of foliations. Accordingly, we discuss how all of these concepts and results apply to Lorentzian orbifolds, insofar as these can be seen as leaf spaces of a specific class of Lorentzian foliations. In particular, we derive an associated Lorentzian timelike diameter theorem on orbifolds. Subjects: Differential Geometry (math.DG) MSC classes: 53C12, 53C50 Cite as: arXiv:2402.05907 [math.DG] (or arXiv:2402.05907v2 [math.DG] for this version) https://doi.org/10.48550/arXiv.2402.05907 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Comm. Analysis and Geom. Vol. 34(3) (2026) Related DOI : https://doi.org/10.4310/CAG.260817233214 Focus to learn more DOI(s) linking to related resources Submission history From: Henrique Amador Puel Martins [ view email ] [v1] Thu, 8 Feb 2024 18:43:32 UTC (66 KB) [v2] Mon, 24 Aug 2026 22:32:39 UTC (81 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2024-02 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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