{
  "abstract": "Élie Cartan established that the metric and intrinsic curvature of a $D$ dimensional embedded manifold $M$ could be determined by tracing the response of another surface $N$ of the same dimensionality, as it is rolled without slipping and twisting on $M$. In the context of spacetime geometry, this construction underpins the MacDowell-Mansouri formulation of General Relativity. We consider extensions of this framework that correspond to rolling of a shape with twisting and with shape evolution; it is shown that these naturally describe torsion and non-metricity respectively. Cartan-geometric formulations of teleparallel gravity and symmetric teleparallelism are discussed in addition to further manifestations of non-metricity in first-order formulations of gravity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30093",
  "author_total": 4,
  "authors": [
    {
      "name": "Damianos Iosifidis"
    },
    {
      "name": "Tomi Koivisto"
    },
    {
      "name": "Wit Krośnicki"
    },
    {
      "name": "Tom Zlosnik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bcsbr1pg9qhrk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30093",
  "fulltext_url": null,
  "id": "bcsbr1pg9qhrk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30093",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214372230",
  "pdf_url": "https://arxiv.org/pdf/2609.30093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bcsbr1pg9qhrk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.30093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30093"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "A Cartan-geometrical perspective on torsion and non-metricity",
  "title_text": "A Cartan-geometrical perspective on torsion and non-metricity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/bcsbr1pg9qhrk",
  "venue": "arXiv",
  "versions": []
}