A characterization of the complex Euclidean space by its holomorphic automorphism group

复欧几里得空间的全纯自同构群的表征

• 批准号: 14540165
• 负责人: KODAMA Akio
• 金额: $ 2.3万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540165/
• 关键词: automorphism group; holomorphically equivalent; topological group; stein manifold; dynamical system; Riemann surface; Value distribution theory

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.

1.Kodama和Shimizu研究了复流形用其全纯自同构群Aut(M)表征的一个基本问题。特别地，他们澄清了Aut(M)同构于Aut（C^ kx (C^*)^l）为拓扑群的复流形M的结构；作为该方法的一个应用，他们还得到了关于复流形的结构的一些新结果，这些结果承认酉群的直积具有全纯作用。Okuyama研究了有理函数和超越全函数的点的无理性无关环的线性化问题，得到了一些新的基本结果。Imayoshi研究了Riemann曲面全纯族的单态问题，得到了一些新的结果。Noguchi研究了全纯曲线的值分布和有理点，得到了新的结果。期望他的结果在小林双曲流形的研究中有广泛的应用。

项目成果

Path integral for the radial Dirac equation

径向狄拉克方程的路径积分

• 发表时间: 2005
• 期刊: Journal of Mathematical Physics 46
• 作者: K.Ogawa;Y.Koyama;S.Oda;Takahiko Nakazi;Takashi Ichinose
• 通讯作者: Takashi Ichinose

Atsushi Kasue: "Convergence of Riemannian manifolds and Laplace operators. I"Ann.l'Institute Fourier. 52. 1219-1257 (2002)

Atsushi Kasue：“黎曼流形和拉普拉斯算子的收敛。I”Ann.lInstitute Fourier。

、A group-theoretic characterization of the space obtained by omitting the coordinate hyperplanes from the complex Euclidean space,

, 通过从复欧几里得空间中省略坐标超平面而获得的空间的群论表征，

• 发表时间: 2006
• 期刊: J. Math. Soc. Japan 58
• 作者: 清水悟;児玉秋雄
• 通讯作者: 児玉秋雄

Takashi Ichinose, Brian Jefferies: "The propagator of the radial Dirac equation"J.Math.Phys.. 43. 3963-3983 (2002)

Takashi Ichinose，Brian Jefferies：“径向狄拉克方程的传播器”J.Math.Phys.. 43. 3963-3983 (2002)

A reducibility problem for monodromy of some surface bundles

一些面丛单性的可约化问题

• 发表时间: 2004
• 期刊: J. of Knot Theory and its Ramifications 13-5
• 作者: FUJIWARA;Koji;Papasogla;Y.Imayoshi
• 通讯作者: Y.Imayoshi