{
  "abstract": "We construct closed Levi non-degenerate CR manifolds with non-vanishing Chern monomials. For every $n \\geq 2$ and $\\lceil n / 4 \\rceil \\leq m \\leq \\lfloor n / 2 \\rfloor$, there exists a $(2 n + 1)$-dimensional example of signature $(\\lfloor n / 2 \\rfloor, \\lceil n / 2 \\rceil)$ on which all Chern monomials with positive indices at most $m$ and total weight at most $n - m$ are non-zero in cohomology with real coefficients. Taking $m = \\lceil n / 4 \\rceil$ gives examples with $c_{1}^{\\lfloor 3 n / 4 \\rfloor} \\neq 0$. For $n = 4$ or $n \\geq 6$, the latter examples show that the Chern-class vanishing theorem for strictly pseudoconvex CR manifolds does not extend to the Levi non-degenerate case. In these dimensions, their underlying manifolds admit no strictly pseudoconvex CR structures. The construction uses circle bundles over products of integral pseudo-Kähler manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12785",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuya Takeuchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avmq8802yvsdf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12785",
  "fulltext_url": null,
  "id": "avmq8802yvsdf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12785",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7221559709",
  "pdf_url": "https://arxiv.org/pdf/2610.12785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avmq8802yvsdf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Chern classes of Levi non-degenerate CR manifolds",
  "title_text": "Chern classes of Levi non-degenerate CR manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/avmq8802yvsdf",
  "venue": "arXiv",
  "versions": []
}