2012 Fiscal Year Final Research Report
Geometric structures defined by differential forms (Calabi-Yau structures, generalized Kaeher structures)
| Project/Area Number |
22540082
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 |
GOTO Ryushi 大阪大学, 理学研究科, 教授 (30252571)
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| Co-Investigator(Kenkyū-buntansha) |
OGUISO Keiji 大阪大学, 理学研究科, 教授 (40224133)
FUJIKI Akira 大阪大学, その他部局等, 名誉教授 (80027383)
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| Project Period (FY) |
2010 – 2012
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| Keywords | からビーヤオ多様体 / 変形理論 / 一般化された幾何構造 / 双エルミート構造 / 一般化されたケーラー構造 / ポアソン構造 |
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| Research Abstract |
We obtain the following three results:
(1) Constructions of generalized Kaehler structures and unobstructed deformations:We established the stability theorem of generalized Kahler structures and constructed many interesting examples. As an application, we showed that there exists a non-trivial bihermitian structure on compact Kahler surfaces with non-zero holomorphic Poisson structures.
(2) New constructions of generalized complex 4-manifolds by logarithmic transformations:We explored the construction to apply arbitrary logarithmic transformations and obtain interesting generalized complex 4-manifods with arbitrary large number of type changing loci.
(3) Constructions of generalized Calabi-Yau metrics and generalized hyperKaehler structures:
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