2009 Fiscal Year Final Research Report
Study of special domains and its application to complex geometry
| Project/Area Number |
18540154
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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 |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
SHIMIZU Satoru Tohoku University, 大学院・理学研究科, 准教授 (90178971)
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| Co-Investigator(Kenkyū-buntansha) |
KODAMA Akio 金沢大学, 理工研究域数物科学系, 教授 (20111320)
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| Co-Investigator(Renkei-kenkyūsha) |
NAKAGAWA Yasuhiro 金沢大学, 理工研究域数物科学系, 准教授 (90250662)
OGATA Shouetu 東北大学, 大学院・理学研究科, 准教授 (90177113)
URAKAWA Hajime 東北大学, 国際教育院, 教授 (50022679)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 関数論 / 特殊領域 / ラインハルト領域 / チューブ領域 / 複素幾何学 / トーラス作用 / リー群 / 正則ベクトル場 |
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| Research Abstract |
In the present research, through the study of special domains, we tried to give a higher-dimensional generalization of the Riemann mapping theorem that is a fundamental and important result in one complex variable. To be concrete, by making use the study of Reinhardt domains that are a kind of special domains, we succeeded in characterizing the direct product B of balls intrinsically by its holomorphic automorphism group when B is of some fundamental types. Also, related to this research, we established a systematic method of investigating the structure of a class of subgroups of the holomorphic automorphism group of the complex Euclidean space, and we obtained a lead to clarifying the structure of G itself.
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Research Products
(15 results)
