{
  "id": "0911.5292",
  "version": "v1",
  "published": "2009-11-27T15:59:59.000Z",
  "updated": "2009-11-27T15:59:59.000Z",
  "title": "Special Conformal Groups of a Riemannian Manifold and Lie Point Symmetries of the Nonlinear Poisson Equation",
  "authors": [
    "Yuri Bozhkov",
    "Igor Leite Freire"
  ],
  "comment": "Paper submitted for publication",
  "categories": [
    "math.AP",
    "math.MG"
  ],
  "abstract": "We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on $M$ are special subgroups of the conformal group of M. In particular, if the scalar curvature of M vanishes, the projection on M of the Lie point symmetry group of the Poisson equation with critical nonlinearity is the conformal group of the manifold. We illustrate our results by applying them to the Thurston geometries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-27T15:59:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J50",
      "35J20",
      "35J60"
    ],
    "keywords": [
      "nonlinear poisson equation",
      "special conformal groups",
      "riemannian manifold",
      "lie point symmetry group",
      "complete group classification"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2010.04.011",
      "journal": "Journal of Differential Equations",
      "year": 2010,
      "volume": 249,
      "number": 4,
      "pages": 872
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JDE...249..872B"
    }
  }
}