{
  "id": "1109.2343",
  "version": "v1",
  "published": "2011-09-11T19:50:21.000Z",
  "updated": "2011-09-11T19:50:21.000Z",
  "title": "Gradient Yamabe Solitons on Warped Products",
  "authors": [
    "Chenxu He"
  ],
  "comment": "23 pages, 3 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "The special nature of gradient Yamabe soliton equation which was first observed by Cao-Sun-Zhang\\cite{CaoSunZhang} shows that a complete gradient Yamabe soliton with non-constant potential function is either defined on the Euclidean space with rotational symmetry, or on the warped product of the real line with a manifold of constant scalar curvature. In this paper we consider the classification in the latter case. We show that a complete gradient steady Yamabe soliton on warped product is necessarily isometric to the Riemannian product. In the shrinking case, we show that there is a continuous family of complete gradient Yamabe shrinkers on warped products which are not isometric to the Riemannian product in dimension three and higher.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-11T19:50:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C25"
    ],
    "keywords": [
      "warped product",
      "complete gradient steady yamabe soliton",
      "gradient yamabe soliton equation",
      "complete gradient yamabe shrinkers",
      "riemannian product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2343H"
    }
  }
}