2009 Fiscal Year Final Research Report
Geometrtic structures defined by differential forms (Topological Calibrations)
| Project/Area Number |
19540079
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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 Osaka University, 大学院・理学研究科, 准教授 (30252571)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIKI Akira 大阪大学, 大学院・理学研究科, 教授 (80027383)
MABUCHI Toshiki 大阪大学, 大学院・理学研究科, 教授 (80116102)
NAMIKAWA Yoshinori 京都大学, 大学院・理学研究科, 教授 (80228080)
FUKAYA Kenji 京都大学, 大学院・理学研究科, 教授 (30165261)
YOSHIKAWA Kenichi 京都大学, 大学院・理学研究科, 教授 (20242810)
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| Project Period (FY) |
2007 – 2009
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| Keywords | カラビーヤオ多様体 / 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 two results:
(1) Constructions of generalized Kaehler structures and unobstructed deformations
We established the stability theorem of generalized Kahler structure and constructed many interesting examples. As an application, we showed that there exists a non-trivial bihermitian structure on compact Kahler surface with non-zero holomorphic Poisson structure.
(2) Calabi-Yau structures on non-compact Kahler manifolds
We showed that there is a Ricci-flat complete kahler metric on each Kahler class of a crepant resolution of normal isolated singularity which is the cone of an Einstein-Sasaki manifold.
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