{
  "abstract": "We compare the Chern holonomy of the first and second Chern-Ricci flows on compact complex manifolds. For the first flow, we construct an explicit immortal pluriclosed solution on a complex two-torus with full and restricted holonomy $U(2)$, except at one finite time when both groups are $U(1)^2$; its smooth limit has holonomy $SU(2)$. The solution is uniformly nondegenerate and has bounds of every fixed differential order for all time. In contrast, the second Chern-Ricci flow preserves full and restricted Chern holonomy under the natural unitary identification, including the initial time and nonclosed groups. The proof combines preservation of a connection reduction, positive-time analyticity, and a path-transport comparison. As an application, the optimal minimum mean curvature on a holomorphic bundle is unchanged when metrics are restricted to any realizable full and restricted holonomy class. An explicit projected-curvature source explains the failure of the corresponding Ricci-flow holonomy argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34665",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuan Liao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxqgzsmh7jsdv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34665",
  "fulltext_url": null,
  "id": "cxqgzsmh7jsdv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34665",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223801180",
  "pdf_url": "https://arxiv.org/pdf/2610.34665",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxqgzsmh7jsdv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34665",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34665"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Chern holonomy under the first and second Chern--Ricci flows",
  "title_text": "Chern holonomy under the first and second Chern--Ricci flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/cxqgzsmh7jsdv",
  "venue": "arXiv",
  "versions": []
}