{
  "abstract": "We classify connected, simply connected, noncompact three-dimensional trans-Sasakian $η$-Einstein manifolds. In [1], we showed that, in the compact case, such a manifold is either of $β$-Kenmotsu type or homothetic to a Sasakian manifold. In this paper, in the noncompact case, we find families of trans-Sasakian $η$-Einstein manifolds that are neither $β$-Kenmotsu nor homothetic to Sasakian manifolds. These families have infinitely many degrees of freedom. We give these nontrivial metrics explicitly. We also give a structure theorem for the case in which the characteristic vector field is Palais-nonregular.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39971",
  "author_total": 1,
  "authors": [
    {
      "name": "Satsuki Matsuno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5pk91x043wv25.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39971",
  "fulltext_url": null,
  "id": "5pk91x043wv25",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39971",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39971",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5pk91x043wv25.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39971",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39971"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Three-dimensional noncompact trans-Sasakian $η$-Einstein manifolds",
  "title_text": "Three-dimensional noncompact trans-Sasakian η-Einstein manifolds",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/5pk91x043wv25",
  "venue": "arXiv",
  "versions": []
}