{
  "abstract": "This paper provides a classification of analytic actions of the semi-orthogonal groups $\\text{SO}^\\circ(p,1)$ and $\\text{SO}^\\circ(p,2)$, for $p \\geq 3$, on closed, connected manifolds of dimension $p$ and $p+1$ respectively. It is a sequel to a previous paper, which treats the case $p,q \\geq 3$. Adapting Uchida's methods, we explicitly construct analytic actions of $\\text{SO}^\\circ(p,1)$ on $\\text{S}^{p}$ and $\\text{S}^{p-1} \\times \\text{S}^{1}$, and analytic actions of $\\text{SO}^\\circ(p,2)$ on $\\text{S}^{p+1}$, $\\text{S}^{p} \\times \\text{S}^{1}$ and $\\text{S}^{p-1} \\times \\text{S}^{2}$, and we classify them up to analytic isomorphism, using a result of Hitchin and Schneider's classification of analytic $\\text{SL}_2(\\mathbb{R})$ actions on surfaces. The main result demonstrates that any analytic $\\text{SO}^\\circ(p,q)$ action, $q=1,2$, on a closed, connected $(p+q-1)$-dimensional manifold is covered by one of the constructed actions or by an action on $\\text{SO}^\\circ(p,q) \\times_P \\text{S}^1$, where $P$ is a maximal parabolic subgroup of $\\text{SO}^\\circ(p,q)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08149",
  "author_total": 1,
  "authors": [
    {
      "name": "Spyridon Lentas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95fc81qaxv6d6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08149",
  "fulltext_url": null,
  "id": "95fc81qaxv6d6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08149",
  "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.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08149",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95fc81qaxv6d6.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08149",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08149"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Classification of analytic $\\text{SO}^o(p,q)$-actions on closed $(p+q-1)$-dimensional manifolds II : $p \\geq 3$, $q=1,2$",
  "title_text": "Classification of analytic SO^o(p,q)-actions on closed (p+q−1)-dimensional manifolds II : p ≥ 3, q=1,2",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/95fc81qaxv6d6",
  "venue": "arXiv",
  "versions": []
}