| Project/Area Number |
12440019
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Osaka University |
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Principal Investigator |
FUJIKI Akira Osaka University, Graduate school of Science, Professor, 大学院・理学研究科, 教授 (80027383)
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| Co-Investigator(Kenkyū-buntansha) |
GOTO Ryushi Osaka University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30252571)
MIYANISHI Masayoshi Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80025311)
MABUCHI Toshiki Osaka University, Graduate school of Science, Professor, 大学院・理学研究科, 教授 (80116102)
HONDA Nobuhiro Hiroshima University, Graduate School of Science, Assistant professor, 大学院・理学研究科, 助手 (60311809)
NAMIKAWA Yoshinori Osaka University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (80228080)
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| Project Period (FY) |
2000 – 2002
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| Keywords | twistor space / self-dual manifold / complex manifold / algebraic dimension / scalar curvature / group action / Doady space / hyperkahler manifold |
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| Research Abstract |
1. We have solved a conjecture of Joyce to the effect that (S^1 × S^1)-invariant self-dual metrics are essentially those constructed by Joyce, by determining the structure of the associated twistor space in detail.
2. For a twistor space Z with algebraic dimension a(Z) = 2 we have shown that either M 〜 mP^2 or M 〜 (S^1 × S^3)#mP^2 for some of its finite unramified covering M^^〜. A similar result is obtained also for the case a(Z) = 1 and of +-type.
3. For a twistor space Z with a(Z) = 2 corresponding to 4P^2 we have done a detailed study of the structure of its algebraic reduction. Honda obtained significant results on the structure and existence of twistor spaces admitting an S^1-action (not necessarily semifree) in the case M = 3P^2, 4P^2.
4. For any m【greater than or equal】5, by considering the deformations of Joyce twistor spaces we have obtained the first examples of a twistor space with a = 2. When m = 4 the construction gives also examples which are different from those constructed by Campana-Kreussler.
5. The Case M = (S^1 × S^3)#mP^2 of +-type: When m = 0 we have completely determined the structure of algebraic reduction of Z. Whe m > 0, we have solved affirmatively the a(Z) = 1-conjecture by LeBrun for the LeBrun families which are the unique explicit example in this case. Meantime, we get a detailed description of the structure of Z.
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