2011 Fiscal Year Final Research Report
Complex structures on compact and non-compact homogeneous spaces
| Project/Area Number |
21540073
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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 | Niigata University |
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Principal Investigator |
HASEGAWA Keizo 新潟大学, 人文社会・教育科学系, 教授 (00208480)
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| Co-Investigator(Kenkyū-buntansha) |
KAMISHIMA Yoshinobu 首都大学東京, 理工学研究科, 教授 (10125304)
ISHI Hideyuki 名古屋大学, 多元数理科学研究科, 准教授 (00326068)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMADA Takumi 島根大学, 総合理工学部, 講師 (40403117)
KOBAYASHI Ryoichi 名古屋大学, 多元数理科学研究科, 教授 (20162034)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 複素多様体 / 等質空間 / 概複素構造 / ケーラー構造 / 局所共形ケーラー構造 |
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| Research Abstract |
In the field of complex geometry on homogeneous manifolds, we have been studying extensions of Kaehler structures to non-Kaehler structures, such as pseudo-Kaehler structures, locally conformally Kaehler structures, and an extension of bounded symmetric domains to non-symmetric or unbounded homogeneous domains. We have obtained some basic results including a structures theorem of homogeneous locally conformally Kaehler manifolds and a classification of four dimensional locally homogeneous locally conformally Kaehler manifolds.
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