A Kummer type construction of self-dual metrics on the connected sum of four complex projective planes

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We show that there exist on 4\bm{CP}<SUP>2</SUP>, the connected sum of four complex projective planes, self-dual metrics with the following properties: (i) the sign of the scalar curvature is positive, (ii) the identity component of the isometry group is U(1), (iii) the metrics are not conformally isometric to the self-dual metrics constructed by LeBrun [{LB1}]. These are the first examples of self-dual metrics with non semi-free U(1)-isometries on simply connected manifolds. Our proof is based on the twistor theory: we use an equivariant orbifold version of the construction of Donaldson and Friedman [{DF}]. We also give a rough description of the structure of the algebraic reduction of the corresponding twistor spaces.

収録刊行物

  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 52(1), 139-160, 2000-01 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10004480051
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    4974662
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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