{
  "abstract": "Let $(M,g)$ be a compact oriented Einstein four-manifold with Einstein constant $E$ and let $\\widehat{R}^+$ denote the action of the Riemann curvature tensor on self-dual two-forms. We show that if $\\widehat{R}^+ < 0$, then $g$ is strictly linearly stable for the Einstein-Hilbert functional, thus giving a chiral criterion for stability. Our result is stronger than the one by Fine-Krasnov-Singer, who conclude local rigidity from $\\widehat{R}^+ < 0$ by proving stability for a different action functional. Our proof proceeds by showing that $(M,g)$ admits a natural spin$^h$ structure carrying a non-zero parallel spin$^h$-spinor. We then apply a lower bound on the Lichnerowicz Laplacian on traceless symmetric two-tensors in the presence of such a spinor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15159",
  "author_total": 1,
  "authors": [
    {
      "name": "Diego Artacho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8kts70ygjj0fs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15159",
  "fulltext_url": null,
  "id": "8kts70ygjj0fs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15159",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7213314394",
  "pdf_url": "https://arxiv.org/pdf/2609.15159",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8kts70ygjj0fs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15159",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15159"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stability of Einstein 4-manifolds satisfying a chiral curvature condition",
  "title_text": "Stability of Einstein 4-manifolds satisfying a chiral curvature condition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8kts70ygjj0fs",
  "venue": "arXiv",
  "versions": []
}