{
  "id": "0810.3195",
  "version": "v1",
  "published": "2008-10-17T16:51:48.000Z",
  "updated": "2008-10-17T16:51:48.000Z",
  "title": "Kahler-Einstein Structures of General Natural Lifted Type on the Cotangent Bundles",
  "authors": [
    "S. L. Druta"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the conditions under which the cotangent bundle $T^*M$ of a Riemaannian manifold $(M,g)$, endowed with a K\\\"ahlerian structure $(G,J)$ of general natural lift type (see \\cite{Druta1}), is Einstein. We first obtain a general natural K\\\"ahler-Einstein structure on the cotangent bundle $T^*M$. In this case, a certain parameter, $\\lambda$ involved in the condition for $(T^*M,G,J)$ to be a K\\\"ahlerian manifold, is expressed as a rational function of the other two, the value of the constant sectional curvature, $c$, of the base manifold $(M,g)$ and the constant $\\rho$ involved in the condition for the structure of being Einstein. This expression of $\\lambda$ is just that involved in the condition for the K\\\"ahlerian manifold to have constant holomorphic sectional curvature (see \\cite{Druta2}). In the second case, we obtain a general natural K\\\"ahler-Einstein structure only on $T_0M$, the bundle of nonzero cotangent vectors to $M$. For this structure, $\\lambda$ is expressed as another function of the other two parameters, their derivatives, $c$ and $\\rho$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-17T16:51:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "53C15",
      "53C07"
    ],
    "keywords": [
      "general natural lifted type",
      "cotangent bundle",
      "kahler-einstein structures",
      "constant holomorphic sectional curvature",
      "general natural lift type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.3195D"
    }
  }
}