{
  "id": "1503.07079",
  "version": "v1",
  "published": "2015-03-24T15:35:23.000Z",
  "updated": "2015-03-24T15:35:23.000Z",
  "title": "The Alekseevskii conjecture in low dimensions",
  "authors": [
    "Romina M. Arroyo",
    "Ramiro A. Lafuente"
  ],
  "comment": "19 pages, 1 table",
  "categories": [
    "math.DG"
  ],
  "abstract": "The long-standing Alekseevskii conjecture states that a connected homogeneous Einstein space G/K of negative scalar curvature must be diffeomorphic to R^n. This was known to be true only in dimensions up to 5, and in dimension 6 for non-semisimple G. In this work we prove that this is also the case in dimensions up to 10 when G is not semisimple. For arbitrary G, besides 5 possible exceptions, we show that the conjecture holds up to dimension 8.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-24T15:35:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C30"
    ],
    "keywords": [
      "low dimensions",
      "connected homogeneous einstein space g/k",
      "long-standing alekseevskii conjecture states",
      "conjecture holds",
      "negative scalar curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150307079A"
    }
  }
}