{
  "abstract": "We study infinitesimally homogeneous affine manifolds with prescribed structure groups. First, for the real symplectic group $\\operatorname{Sp}(2n,\\mathbb R)$, we prove that the corresponding infinitesimally homogeneous structures are precisely flat torsion-free symplectic affine structures. Second, for \\(\\operatorname{U}(n)\\times\\{1\\}\\), whose \\(G\\)-structures are equivalent to almost contact metric data, we classify the torsion-free characteristic tensors and obtain the general torsional case by invariant deformation. The admissible torsion and inner-torsion parameters are governed by a single algebraic relation, and the horizontal distribution is contact precisely when a certain combination of these parameters does not vanish. We also describe the compatible connections and relate the torsion-free branches to trans-Sasakian geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19568",
  "author_total": 2,
  "authors": [
    {
      "name": "Carlos Alberto Marín Arango"
    },
    {
      "name": "Alejandro Pinilla Barrera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pt7z332gm6ed.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19568",
  "fulltext_url": null,
  "id": "7pt7z332gm6ed",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19568",
  "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": "W7213605116",
  "pdf_url": "https://arxiv.org/pdf/2609.19568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pt7z332gm6ed.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.19568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19568"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups",
  "title_text": "Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/7pt7z332gm6ed",
  "venue": "arXiv",
  "versions": []
}