{
  "abstract": "Following Miyamoto, we consider Q-charts, a class of subductions $ϕ\\colon X\\to Y$ of diffeological spaces along which Blohmann's elasticity descends. We show that the Riemannian apparatus of elastic diffeology---vertical, horizontal and full connections, Riemannian metrics, Levi-Civita connections and geodesics---also descends along Q-charts. More precisely, structures on $Y$ correspond bijectively to structures on $X$ that are invariant under the pseudogroup $Ψ(ϕ)$ of fibre-preserving transitions, and torsion-freeness, effectivity, flatness, fullness, the Levi-Civita property and the geodesic equation are preserved in both directions. The key input is that the iterated tangent bundles $T^nX$ and their fibre products $T_kX$ are the pullbacks along $ϕ$ of the corresponding bundles over $Y$. For quotients by principal actions of diffeologically discrete groups, we lift geodesics globally, prove that the class of elastic spaces on which $\\R$ is a curve object is closed under such quotients, and show that complete geodesic flows descend. As an application, we determine the Riemannian geometry of the irrational tori $\\Tor_α=\\R/(\\Z+α\\Z)$ completely. Let $\\vartheta$ be the one-form on $\\Tor_α$ induced by $dt$ on $\\R$. Every Riemannian metric is a positive constant multiple of $\\vartheta^2$, and the vertical connections form a one-parameter family of flat effective connections, a single member of which is the unique Levi-Civita connection of every metric. This connection has a complete geodesic flow, yet the induced pseudo-distance vanishes identically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01346",
  "author_total": 1,
  "authors": [
    {
      "name": "Yusuke Shiobara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9hsa63chydjsm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01346",
  "fulltext_url": null,
  "id": "9hsa63chydjsm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01346",
  "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",
      "math.CT"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7216499066",
  "pdf_url": "https://arxiv.org/pdf/2610.01346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hsa63chydjsm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Riemannian Structures on Quotients in Elastic Diffeology via Q-Charts",
  "title_text": "Riemannian Structures on Quotients in Elastic Diffeology via Q-Charts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/9hsa63chydjsm",
  "venue": "arXiv",
  "versions": []
}