{
  "abstract": "We introduce a class of generalised Killing spinors, termed affine Killing spinors (AKS), for which the associated endomorphism is a constant linear combination of the Ricci endomorphism and the identity map. We classify Riemannian spin manifolds admitting an AKS under two additional curvature hypotheses: harmonic curvature and local conformal flatness. Furthermore, we characterise Riemannian spin manifolds that admit a non-zero parallel one-form and an AKS. Additionally, we prove that in dimension three every curvature-homogeneous manifold carrying an AKS is locally homogeneous. Finally, we provide a complete classification of three-dimensional Lie groups equipped with a Bianchi metric admitting an invariant AKS.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29274",
  "author_total": 2,
  "authors": [
    {
      "name": "Diego Artacho"
    },
    {
      "name": "Jihun Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bq7zj52p6chpy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29274",
  "fulltext_url": null,
  "id": "bq7zj52p6chpy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29274",
  "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",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214306328",
  "pdf_url": "https://arxiv.org/pdf/2609.29274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bq7zj52p6chpy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A class of generalised Killing spinors determined by the Ricci tensor and the metric",
  "title_text": "A class of generalised Killing spinors determined by the Ricci tensor and the metric",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/bq7zj52p6chpy",
  "venue": "arXiv",
  "versions": []
}