Study of holomorphic foliations and vector fields
| Project/Area Number |
19684001
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
ASUKE Taro The University of Tokyo, 大学院・数理科学研究科, 准教授 (30294515)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥7,800,000 (Direct Cost: ¥6,000,000、Indirect Cost: ¥1,800,000)
Fiscal Year 2009: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2008: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
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| Keywords | 葉層構造 / Bott類 / Godbillon-Vey類 / Fatou集合 / Julia集合 / ベクトル場 / 複素構造 / 共形的測度 / 臨界指数 / 特性類 |
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| Research Abstract |
I studied the Godbillon-Vey class of transversely holomorphic foliations, and showed that it is rigid under continuous deformations in the category of transversely holomorphic foliations. It is also shown that an invariant of deformations of foliations is closely related to the rigidity. I also introduced a new, simple definition of Fatou and Julia sets of transversely holomorphic foliations. A classification of Fatou components and some fundamental properties concerning invariant metics and conformal measures are obtained.
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Report
(4 results)
Research Products
(29 results)
