A study on the structure of complex ellipsoids

复杂椭球结构的研究

• 批准号: 12640162
• 负责人: KODAMA Akio
• 金额: $ 1.98万
• 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: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640162/
• 关键词: bounded domain; automorphism group; complex ellipsoid; spherical boundary point; hyperbolic hypersurface; tube domain; equivalence problem; 双正則同値; スタイン多様体; CR同値

The main purpose of this research is to solve the following fundamental con jecture : "Let D be a bounded domain in an n-dimensional complex Euclidean space C^n with non-compact automorphism group Aut(D). Then D is necessarily biholomorphic to some complex ellipsoidal domain E". Concerning this research, we studied and obtained the following :1. Kodama studied the structure of the set consisting of all non-unbilical points of a given complex ellipsoid E, and he applied his ideas to the characteri zation of complex ellipsoids with spherical boundary points.2. Fujimoto studied Nevanlinna theory of holomorphic mappings into the complex projective spaces P^nc, and obtained some new results on hyperbolic hypersurfaces in P^3c of degree 8.3. Shimizu studied the Lie algebra of polynomial vector fields on a tube domain T_Ω in C^n. He obtained Prolongation Theorem for such vector fields and solved the equivalence problem for tube domains.

本研究的主要目的是解决如下基本猜想：“设D是n维复欧氏空间C^n中具有非紧自同构群Aut(D)的有界区域，则D必然双全纯于某个复椭球区域E”。关于这项研究，我们研究并得到了如下结果：1.小玉研究了给定的复椭球体E的所有非脐点组成的集合的结构，并将他的思想应用于刻画具有球面边界点的复椭球体。Fujimoto研究了复射影空间P^Nc中全纯映射的Nevanlinna理论，得到了关于P^3c中8.3次双曲超曲面的一些新结果。清水研究了C^n中管域T_Ω上多项式向量场的李代数，得到了这类向量场的延拓定理，解决了管域的等价问题。

项目成果

Atsushi Kasue: "Convergence of Riemanian manifolds and Laplace operators, I"Ann. Institut Fourier. 52(未定). (2002)

Atsushi Kasue：“黎曼流形和拉普拉斯算子的收敛，I”Ann。52（TBD）。

S.Shimizu: "A classification of two-dimensional tube domains"Amer.J.Math.. 122. 1289-1308 (2000)

S.Shimizu：“二维管域的分类”Amer.J.Math.. 122. 1289-1308 (2000)

Satoru Shimizu: "A classification of two-dimensional tube domains"Amer. J. Math.. 122. 1289-1308 (2000)

Satoru Shimizu：“二维管域的分类”Amer。

Takashi Ichinose and Hideo Tamura: "The norm convergence of the Trotter-kato product formula with error bound"Commun.Math.Phys.. (未定).

Takashi Ichinose 和 Hideo Tamura：“具有误差界的 Trotter-kato 乘积公式的范数收敛性”Commun.Math.Phys..（待定）。

Junjiro Noguchi: "The second main theorem for holomorphic curves into semi-Abelian varieties"Acta Math.. 188(未定). (2002)

Junjiro Noguchi：“半阿贝尔簇全纯曲线的第二个主要定理”Acta Math.. 188（TBD）（2002）。