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)
満渕 俊樹 大阪大学, 理学研究科, 教授 (80116102)
梅原 雅顕 大阪大学, 理学研究科, 教授 (90193945)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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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 / カラビーヤオ構造 / 一般化された複素構造 / 一般化されたケーラ－構造 / 一般化された超ケーラ－構造 / ４次元多様体の対数変換 / リッチ平坦計量 / 一般化された幾何学 / 接触構造 / 佐々木構造 / リッチ平坦ケーラー計量 / ノン-ケーラー多様体_ / 局所等角ケーラー構造 |
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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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Report
(4 results)
Research Products
(14 results)
