2001 Fiscal Year Final Research Report Summary
A study on the structure of complex ellipsoids
| Project/Area Number |
12640162
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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, Fac of Sci., Professor, 理学部, 教授 (20111320)
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| Co-Investigator(Kenkyū-buntansha) |
KASUE Atsushi Kanazawa University, Fac of Sci., Professor, 理学部, 教授 (40152657)
ICHINOSE Takashi Kanazawa University, Fac of Sci., Professor, 理学部, 教授 (20024044)
FUJIMOTO Hirotaka Kanazawa University, Fac of Sci., Professor, 理学部, 教授 (60023595)
SHIMIZU Satoru Tohoku Univ., Grad. School, Assoc. Prof., 理学研究科, 助教授 (90178971)
NOGUCHI Junjiro Univ. of Tokyo, Grand. School of Math. Sci., Professor, 数理科学研究科, 教授 (20033920)
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| Project Period (FY) |
2000 – 2001
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| Keywords | bounded domain / automorphism group / complex ellipsoid / spherical boundary point / hyperbolic hypersurface / tube domain / equivalence problem |
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| Research Abstract |
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.
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