{
  "abstract": "Let $M^5$ be an oriented real hypersurface of a six-dimensional strict nearly Kähler manifold $(\\widetilde M^6,\\widetilde g,J)$, and let $ξ=-JN$ and $η=g(\\,\\cdot\\,,ξ)$ denote the induced Reeb field and Reeb one-form. We prove the pointwise obstruction \\[ (dη)_p\\neq0\\qquad\\text{for every }p\\in M. \\] The proof is local and uses only the hypersurface identity \\[ \\nabla_Xξ=ϕAX-G(X,N) \\] together with the six-dimensional strict nearly Kähler algebra. If $(dη)_p=0$, then \\[ ϕA+Aϕ=2G_N,\\qquad G_NX=G(X,N), \\] which forces the Hopf condition. On the contact hyperplane $\\mathcal D_p=\\kerη_p$, the endomorphism $ϕA+Aϕ$ then commutes with $ϕ$, whereas $G_N$ anti-commutes with $ϕ$ and satisfies \\[ G_N^2=-αI_{\\mathcal D_p},\\qquad α>0. \\] This contradiction proves the obstruction. As a connection-theoretic consequence, for the standard Yano semi-symmetric metric connection associated with $ξ$, \\[ \\widehat\\nabla_XY=\\nabla_XY+η(Y)X-g(X,Y)ξ, \\] one has in dimension five \\[ \\operatorname{Skew}\\operatorname{Ric}^{\\widehat\\nabla}=-\\frac32\\,dη, \\] and hence $\\operatorname{Ric}^{\\widehat\\nabla}$ is nowhere symmetric. The obstruction also rules out any local induced almost contact class whose defining conditions include $dη=0$. We illustrate the result on the standard homogeneous strict nearly Kähler spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00078",
  "author_total": 2,
  "authors": [
    {
      "name": "Jae Won Lee"
    },
    {
      "name": "Chul Woo Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/76ka1r2ravn27.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00078",
  "fulltext_url": null,
  "id": "76ka1r2ravn27",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00078",
  "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/2610.00078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/76ka1r2ravn27.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Quantitative Reeb-Form Obstruction for Real Hypersurfaces of Strict Nearly Kähler Six-Manifolds",
  "title_text": "A Quantitative Reeb-Form Obstruction for Real Hypersurfaces of Strict Nearly Kähler Six-Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/76ka1r2ravn27",
  "venue": "arXiv",
  "versions": []
}