{
  "id": "1408.1078",
  "version": "v2",
  "published": "2014-08-05T19:53:28.000Z",
  "updated": "2015-04-28T10:01:54.000Z",
  "title": "Einstein Metrics, Harmonic Forms, and Symplectic Four-Manifolds",
  "authors": [
    "Claude LeBrun"
  ],
  "comment": "in Annals of Global Analysis and Geometry (2015)",
  "doi": "10.1007/s10455-015-9458-0",
  "categories": [
    "math.DG",
    "math.SG"
  ],
  "abstract": "If $M$ is the underlying smooth oriented $4$-manifold of a Del Pezzo surface, we consider the set of Riemannian metrics $h$ on $M$ such that $W^+(\\omega , \\omega )> 0$, where $W^+$ is the self-dual Weyl curvature of $h$, and $\\omega$ is a non-trivial self-dual harmonic $2$-form on $(M,h)$. While this open region in the space of Riemannian metrics contains all the known Einstein metrics on $M$, we show that it contains no others. Consequently, it contributes exactly one connected component to the moduli space of Einstein metrics on $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-05T19:53:28.000Z",
      "abstract": "Let M be the underlying 4-manifold of a Del Pezzo surface. We show that a specific open region in the space of Riemannian metrics on M contains all the known Einstein metrics on M, but no others; consequently, this region contributes exactly one connected component to the moduli space of Einstein metrics on M. Our methods also yield new results concerning the geometry of almost-Kaehler 4-manifolds.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-28T10:01:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "14J45",
      "53A30",
      "53C57"
    ],
    "keywords": [
      "einstein metrics",
      "symplectic four-manifolds",
      "harmonic forms",
      "del pezzo surface",
      "specific open region"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1309947,
      "adsabs": "2014arXiv1408.1078L"
    }
  }
}