{
  "id": "0806.3572",
  "version": "v1",
  "published": "2008-06-22T15:16:26.000Z",
  "updated": "2008-06-22T15:16:26.000Z",
  "title": "Secure two-dimensional tori are flat",
  "authors": [
    "Victor Bangert",
    "Eugene Gutkin"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "A riemannian manifold is secure if the geodesics between any pair of points in the manifold can be blocked by a finite number of point obstacles. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. The conjecture claims, in particular, that a riemannian torus of any dimension is secure if and only if it is flat. We prove this for two-dimensional tori.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-22T15:16:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D40",
      "37E99",
      "53C22"
    ],
    "keywords": [
      "secure two-dimensional tori",
      "compact riemannian manifolds",
      "conjecture claims",
      "finite number",
      "point obstacles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.3572B"
    }
  }
}