{
  "abstract": "We fix a smooth vector field and a positive parameter $m$, and compare the nondegenerate metrics for which the field is conformal or $m$-modified conformal with the same prescribed smooth factor. Metrics of arbitrary signature are allowed. Passing to inverse metrics gives a linear transport equation and an explicit correspondence on the exact nondegeneracy domains. At a regular point, transverse initial data yield a signature-preserving correspondence of metric germs. For a nowhere-zero field and a Killing background in dimension at least three, every metric satisfying the modified conformal equation and differing from the background by a tensor of rank at most one has factor zero; its inverse-metric difference is $rX\\otimes X$ for a unique smooth function $r$. Under a complete flow, such global deformations exist precisely when the field is null for the background and admits a smooth function $τ$ with $Xτ=1$. An auxiliary field satisfying $[X,Z]=X$ gives a second correspondence under orthogonality assumptions. Finally, for a nowhere-zero complete field, a Killing metric and a zero-factor modified conformal metric have inverse-metric difference of rank at least two whenever that rank is constant. In the rank-two case, the pair determines a unique auxiliary field. Examples distinguish the roles of dimension, completeness, constant rank, the zero-factor condition, and orthogonality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00844",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhigang Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ff1jrn2cmefx0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00844",
  "fulltext_url": null,
  "id": "ff1jrn2cmefx0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00844",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00844",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ff1jrn2cmefx0.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00844",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00844"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Metric Correspondences and Low-Rank Deformations for Conformal and \\(m\\)-Modified Conformal Vector Fields",
  "title_text": "Metric Correspondences and Low-Rank Deformations for Conformal and m-Modified Conformal Vector Fields",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/ff1jrn2cmefx0",
  "venue": "arXiv",
  "versions": []
}