{
  "id": "1501.03414",
  "version": "v1",
  "published": "2015-01-14T17:17:56.000Z",
  "updated": "2015-01-14T17:17:56.000Z",
  "title": "Biharmonic and f-biharmonic maps from a 2-sphere",
  "authors": [
    "Ze-Ping Wang",
    "Ye-Lin Ou",
    "Han-Chun Yang"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study biharmonic maps and f-biharmonic maps from a round sphere $(S^2, g_0)$, the latter maps are equivalent to biharmonic maps from Riemann spheres $(S^2, f^{-1}g_0)$. We proved that for rotationally symmetric maps between rotationally symmetric spaces, both biharmonicity and f-biharmonicity reduce to a 2nd order linear ordinary differential equation. As applications, we give a method to produce biharmonic maps and f-biharmonic maps from given biharmonic maps and we construct many examples of biharmonic and f-biharmonic maps from a round sphere $S^2$ and between two round spheres. Our examples include non-conformal proper biharmonic maps $(S^2, f^{-1}g_0)\\longrightarrow S^2$ and $(S^2, f^{-1}g_0)\\longrightarrow S^n$, or non-conformal f-biharmonic maps $(S^2, g_0)\\longrightarrow S^2$ and $(S^2,g_0)\\longrightarrow S^n$ from round sphere with two singular points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-14T17:17:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "round sphere",
      "2nd order linear ordinary differential",
      "order linear ordinary differential equation",
      "non-conformal proper biharmonic maps",
      "non-conformal f-biharmonic maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150103414W"
    }
  }
}