{
  "id": "1704.04944",
  "version": "v1",
  "published": "2017-04-17T12:32:23.000Z",
  "updated": "2017-04-17T12:32:23.000Z",
  "title": "On the fundamental group of semi-Riemannian manifolds with positive curvature operator",
  "authors": [
    "Jun-ichi Mukuno"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "This paper presents an investigation of the relation between some positivity of the curvature and the finiteness of fundamental groups in semi-Riemannian geometry. We consider semi-Riemannian submersions $\\pi : (E, g) \\rightarrow (B, -g_{B}) $ under the condition with $(B, g_{B})$ Riemannian, the fiber closed Riemannian, and the horizontal distribution integrable. Then we prove that, if the lightlike geodesically complete or timelike geodesically complete semi-Riemannian manifold $E$ has some positivity of curvature, then the fundamental group of the fiber is finite. Moreover we construct an example of semi-Riemannian submersions with some positivity of curvature, non-integrable horizontal distribution, and the finiteness of the fundamental group of the fiber.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-17T12:32:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C50",
      "53C21"
    ],
    "keywords": [
      "fundamental group",
      "positive curvature operator",
      "semi-riemannian submersions",
      "timelike geodesically complete semi-riemannian manifold",
      "positivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}