{
  "abstract": "We prove two constant rank theorems for the Ricci tensor in two geometric settings: manifolds with harmonic curvature and gradient Ricci solitons. In both cases, if the $k$-intermediate Ricci curvature satisfies $\\Ric_k\\geq0$ for some $1\\leq k\\leq n-2$, then the Ricci tensor has constant rank and its nullity distribution is parallel. In the complete case, the universal cover splits isometrically along the Ricci-null directions. We also show that the range $1\\leq k\\leq n-2$ is sharp: in every dimension $n\\geq4$, nonnegative Ricci curvature alone does not imply the constant rank property in either setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17691",
  "author_total": 2,
  "authors": [
    {
      "name": "Mijia Lai"
    },
    {
      "name": "Guoqiang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/et0bjw4xmtpgc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17691",
  "fulltext_url": null,
  "id": "et0bjw4xmtpgc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17691",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221755325",
  "pdf_url": "https://arxiv.org/pdf/2610.17691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/et0bjw4xmtpgc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Constant Rank Theorems under Intermediate Ricci Curvature",
  "title_text": "Constant Rank Theorems under Intermediate Ricci Curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/et0bjw4xmtpgc",
  "venue": "arXiv",
  "versions": []
}