{
  "id": "2210.16448",
  "version": "v1",
  "published": "2022-10-29T00:08:15.000Z",
  "updated": "2022-10-29T00:08:15.000Z",
  "title": "Kummer-type constructions of almost Ricci-flat 5-manifolds",
  "authors": [
    "Chanyoung Sung"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "A smooth closed manifold $M$ is called almost Ricci-flat if $\\mu(M)=0$ for $$\\mu(M):=\\inf_g||\\textrm{Ric}_g||_\\infty\\cdot \\textrm{diam}_g(M)^2$$ where $\\textrm{Ric}_g$ and $\\textrm{diam}_g$ denote the Ricci tensor and the diameter of $g$ respectively and $g$ runs over all Riemannian metrics on $M$. By using Kummer-type method we construct a smooth closed almost Ricci-flat nonspin 5-manifold $M$ which is simply connected. It's minimal volume vanishes, namely it collapses with sectional curvature bounded.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-29T00:08:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C25"
    ],
    "keywords": [
      "kummer-type constructions",
      "minimal volume vanishes",
      "kummer-type method",
      "riemannian metrics",
      "smooth closed manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}