{
  "abstract": "In this paper, we establish the decomposition and product theory of $Γ$-symmetric spaces, where $Γ$ is isomorphic to $\\mathbb{Z}_2\\times\\mathbb{Z}_2$. These results lead to the local classification of semisimple Riemannian $\\mathbb{Z}_2\\times\\mathbb{Z}_2$-symmetric spaces of nontrivial type. Furthermore, we identify notable phenomena specific to $\\mathbb{Z}_2\\times\\mathbb{Z}_2$-symmetric spaces: the existence of distinct product structures and that of an example with the trivial infinitesimal isotropy representation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09750",
  "author_total": 1,
  "authors": [
    {
      "name": "Jin Matsui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9cvtdwp44nj52.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09750",
  "fulltext_url": null,
  "id": "9cvtdwp44nj52",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09750",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7212137318",
  "pdf_url": "https://arxiv.org/pdf/2609.09750",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cvtdwp44nj52.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09750",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09750"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Product structures and decompositions of $\\mathbb{Z}_2\\times\\mathbb{Z}_2$-symmetric spaces",
  "title_text": "Product structures and decompositions of ℤ_2×ℤ_2-symmetric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/9cvtdwp44nj52",
  "venue": "arXiv",
  "versions": []
}