{
  "abstract": "We study almost contact metric manifolds that are locally conformal to Sasakian manifolds in the normalization of Olszak. We show that the local conformal factors are uniquely determined by the structure; consequently, every such manifold is globally conformal to a Sasakian manifold and its Lee form is exact. We then investigate the $k$-nullity condition $ R(X,Y)ξ=k\\{η(Y)X-η(X)Y\\}. $ We prove that a smooth nullity function is necessarily constant, including in dimension three. Moreover, the $k$-nullity condition is equivalent to the assertion that $f=\\exp(σ)$ satisfies $ \\mathrm{Hess}_g f=-(kf+C)g $ for a constant $C$, and hence to the fact that the conformal metrics $g$ and $g_0=\\exp(-2σ)g$ have the same geodesic circles. We derive the range of the conformal factor, a local warped-product description, and a classification in the complete case: when the Lee form is nonzero, the complete metric is a simply connected space form of curvature $k$. Finally, we construct incomplete examples of nonconstant sectional curvature in every dimension $2n+1\\geq 5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.12924",
  "author_total": 2,
  "authors": [
    {
      "name": "Fortuné Massamba"
    },
    {
      "name": "Pontsho Moile"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77hkj8wvw6536.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.12924",
  "fulltext_url": null,
  "id": "77hkj8wvw6536",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.12924",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.12924",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77hkj8wvw6536.ris",
  "sources": [
    {
      "first_seen": "2026-11-11T06:21:55Z",
      "native_id": "2611.12924",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.12924"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Conformally Sasakian manifolds and the $k$-nullity condition",
  "title_text": "Conformally Sasakian manifolds and the k-nullity condition",
  "type": "preprint",
  "updated_at": "2026-11-13T06:20:11Z",
  "url": "https://research.draconitic.com/paper/77hkj8wvw6536",
  "venue": "arXiv",
  "versions": []
}