{
  "id": "2003.06850",
  "version": "v1",
  "published": "2020-03-15T15:29:59.000Z",
  "updated": "2020-03-15T15:29:59.000Z",
  "title": "Compactness and index of relative equilibria for the curved n-body problem",
  "authors": [
    "Shuqiang Zhu"
  ],
  "comment": "27 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "For the curved n-body problem, we show that the set of relative equilibrium is away from most singular configurations in H^3, and away from a subset of singular configurations in S^3. We also show that each of the n!/2 geodesic relative equilibria for n masses has Morse index n-2. Then we get a direct corollary that there are at least (3n-4)(n-1)!/2 relative equilibria for given n masses if all relative equilibria of these masses are non-degenerate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-15T15:29:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F10",
      "70F15"
    ],
    "keywords": [
      "relative equilibrium",
      "curved n-body problem",
      "compactness",
      "singular configurations",
      "direct corollary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}