{
  "abstract": "In this article, we introduce the concepts of generalized semi-Riemannian submersions and foliations, extending the classical framework to accommodate leaves with varying or degenerate causal characters, such as homogeneous foliations on semi-Riemannian manifolds and codimension-one lightlike foliations on Lorentz manifolds (including pp-waves). We establish that a regular foliation with a basic horizontal distribution is generalized semi-Riemannian if and only if it is transnormal. Furthermore, we introduce stationary foliations and prove that a stationary transnormal foliation induces a classical Riemannian foliation on the spatial rest space of a conformal observer. As a geometric consequence, we obtain a rigidity result ruling out stationary codimension-one lightlike foliations on positively curved Robertson-Walker spacetimes or static spacetimes. Finally, we derive an O'Neill-type sectional curvature formula for submersions with an involutive total distribution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03951",
  "author_total": 2,
  "authors": [
    {
      "name": "Benigno O. Alves"
    },
    {
      "name": "Jair C. de Oliveira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09b271ymjc8db.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03951",
  "fulltext_url": null,
  "id": "09b271ymjc8db",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03951",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7208789661",
  "pdf_url": "https://arxiv.org/pdf/2609.03951",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09b271ymjc8db.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03951",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03951"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generalized Semi-Riemannian Submersions and Foliations",
  "title_text": "Generalized Semi-Riemannian Submersions and Foliations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/09b271ymjc8db",
  "venue": "arXiv",
  "versions": []
}