2004 Fiscal Year Final Research Report Summary
A characterization of the complex Euclidean space by its holomorphic automorphism group
| Project/Area Number |
14540165
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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 | Kanazawa University |
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Principal Investigator |
KODAMA Akio Kanazawa University, Grad.Sch.of Nat.Sci.& Tec., Prof., 自然科学研究科, 教授 (20111320)
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| Co-Investigator(Kenkyū-buntansha) |
ICHINOSE Takashi Kanazawa University, Grad.Sch.of Nat.Sci.& Tec., Prof., 自然科学研究科, 教授 (20024044)
OKUYAMA Yusuke Kanazawa University, Grad.Sch.of Nat.Sci.& Tec., Lect., 自然科学研究科, 講師 (00334954)
IMAYOSHI Yoichi Osaka City Univ., Grad.Sch.of Sci., Prof., 理学研究科, 教授 (30091656)
NOGUCHI Junjiro Univ.of Tokyo, Grad.Sch.of Math.Sci., Prof., 数理科学研究科, 教授 (20033920)
SHIMIZU Satoru Tohoku Univ., Grad.Sch.of Sci., Assoc.Prof., 理学研究科, 助教授 (90178971)
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| Project Period (FY) |
2002 – 2004
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| Keywords | automorphism group / holomorphically equivalent / topological group / stein manifold / dynamical system / Riemann surface / Value distribution theory |
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| Research Abstract |
1.Kodama and Shimizu studied a fundamental problem on a characterization of complex manifold by its holomorphic automorphism group Aut(M). In particular, they clearified the structure of complex manifold M with Aut(M) isomorphic to Aut(C^k×(C^*)^l) as topological groups ; and also, as an application of their method, they obtained some new results on the structure of complex manifold admitting a holomorphic action of the direct product of unitary groups.
2.Okuyama studied the linearlization problem for irrationally indifferent cycle of points of rational functions and transcendental entire functions, and obtained some new fundamental results.
3.Imayoshi studied some problems on the monodromy of holomorphic families of Riemann surfaces, and he obtained some new results. And, Noguchi studied the value distribution and rational points of holomorphic curves, and obtained new results. It is expected that his results have various applications in the study on Kobayashi hyperbolic manifolds.
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