{
  "id": "math/0302112",
  "version": "v1",
  "published": "2003-02-11T05:50:33.000Z",
  "updated": "2003-02-11T05:50:33.000Z",
  "title": "On dimension reduction in the Kähler-Ricci flow",
  "authors": [
    "Huai-Dong Cao"
  ],
  "comment": "15 pages, Latex",
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider dimension reduction for solutions of the K\\\"ahler-Ricci flow with nonegative bisectional curvature. When the complex dimension $n=2$, we prove an optimal dimension reduction theorem for complete translating K\\\"ahler-Ricci solitons with nonnegative bisectional curvature. We also prove a general dimension reduction theorem for complete ancient solutions of the K\\\"ahler-Ricci flow with nonnegative bisectional curvature on noncompact complex manifolds under a finiteness assumption on the Chern number $c^n_1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-02-11T05:50:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kähler-ricci flow",
      "nonnegative bisectional curvature",
      "general dimension reduction theorem",
      "optimal dimension reduction theorem",
      "noncompact complex manifolds"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2112C"
    }
  }
}