A study on the structure of complex ellipsoids

本研究的主要目的是解决以下基本猜想：“设D是n维复欧几里德空间C^n上具有非紧自同构群Aut(D)的有界区域。”那么D必然是复椭球域E ‘ ’的生物全纯的。在本研究中，我们进行了以下研究：1。Kodama研究了给定的复椭球E的所有非双曲点组成的集合的结构，并将他的思想应用于具有球面边界点的复椭球的表征。Fujimoto研究了复射影空间P^3c的全纯映射的Nevanlinna理论，并在P^3c的8.3次双曲超曲面上得到了一些新的结果。Shimizu研究了C^n管域T_Ω上多项式向量场的李代数。他得到了这类向量场的推广定理，并解决了管域的等价问题。

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.