{
  "abstract": "We show that the data of a Riemannian metric on a differentiable stack presented by an orbifold groupoid is equivalent to the data of a Riemannian metric on its diffeological orbit space. As a consequence, we conclude that the classical notion of Riemannian orbifold is equivalent to that of a Riemannian diffeological orbifold. We use the framework for Riemannian diffeology introduced by Kuribayashi, Sakai, and Shiobara, and our result answers a problem they posed in the affirmative. More generally, we show that a Riemannian metric on a Lie groupoid, namely a 2-metric in the sense of del Hoyo and Fernandes, induces a Riemannian metric on its diffeological orbit space only if the Lie groupoid is regular, and that properness is a sufficient but not necessary condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08939",
  "author_total": 1,
  "authors": [
    {
      "name": "David Miyamoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5s69e5hvth183.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08939",
  "fulltext_url": null,
  "id": "5s69e5hvth183",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08939",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7168169736",
  "pdf_url": "https://arxiv.org/pdf/2607.08939",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5s69e5hvth183.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2607.08939",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08939"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Diffeological Riemannian orbifolds",
  "title_text": "Diffeological Riemannian orbifolds",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/5s69e5hvth183",
  "venue": "arXiv",
  "versions": []
}