{
  "abstract": "We use differential Galois theory to prove that given two arbitrary points $X$ and $Y$ on the Stiefel manifold, there is no closed-form analytic expression for the Riemannian logarithm $\\log_X Y$, the geodesic between $X$ and $Y$, or the geodesic distance between $X$ and $Y$. In other words, these cannot be expressed in terms of elementary functions of the coordinates of $X$ and $Y$; in fact, our result goes further --- even if we allow for repeated integrals of elementary functions, there is still no such expression.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37568",
  "author_total": 2,
  "authors": [
    {
      "name": "Rongbiao Thomas Wang"
    },
    {
      "name": "Lek-Heng Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7fp1wrpscrrqn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37568",
  "fulltext_url": null,
  "id": "7fp1wrpscrrqn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37568",
  "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.OC"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7224076868",
  "pdf_url": "https://arxiv.org/pdf/2610.37568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7fp1wrpscrrqn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37568"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "No closed-form formula for Stiefel geodesics",
  "title_text": "No closed-form formula for Stiefel geodesics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7fp1wrpscrrqn",
  "venue": "arXiv",
  "versions": []
}