2001 Fiscal Year Final Research Report Summary
Value distribution thieory of meromorphic mappings, in particular, uniqueness, degeneracy and normal families of meromorphic mappings
| Project/Area Number |
12640198
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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 | Numazu College of Technology |
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Principal Investigator |
AIHARA Yoshihiro Numazu College of Technology, Division of Liberal Arts, Associate Professor., 教養科, 助教授 (60175718)
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| Co-Investigator(Kenkyū-buntansha) |
KAMADA Hiroyuki Numazu College of Technology, Division of Liberal Arts, Associate Professor., 教養科, 助教授 (00249799)
KITAGAWA Hoshihisa Utsunomiya University, Faculty of Education, Associate Professor., 教育学部, 助教授 (20144917)
MORI Seiki Yamagata University, Faculty of Science, Professor., 理学部, 教授 (80004456)
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| Project Period (FY) |
2000 – 2001
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| Keywords | meromorphic map / unicity theorem / algebraic dependence / Nevanlinna's deficiency / flat torus / indefinite Khaler metric / 不定値計量 |
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| Research Abstract |
The head investigator Aihara has studied the uniqueness problem of meromorphic mappings.
He has investigated the propagation of algebraic dependence of meromorphic mappings. He gave some criteria for dependence of meromorphic mappings from finite sheeted analytic covering spaces over the complex m-space into a projective algebraic manifold and their applications (to appear hi Nagoya Math. J.). In particular, he gave a condition that two holomorphic mappings into a smooth elliptic curve are algebraically related by endomorphisms of elliptic curve. He and a investigator Mori also gave a construction of meromorphic mappings with deficiencies (Deficiencies of meromorphic mappings of hypersurfaces, preprint). An investigator Mori studied an elimination problem of defects of meromorphic mappings and obtained elimination theorems.
An investigator Kitagawa studied isometric deformations of flat tori isometrically immersed hi the 3-sphere S^3 with constant mean curvature. As a result, he obtained a classification of the flat tori isometrically immersed in S^3 which admit no isometric deformation. An investigator Kamada studied the existence problem for self-dual neutral Khaler metrics on compact complex surfaces, and proved that a compact self-dual neutral Khaler surface admitting a certain S^1 symmetry is biholomorphic to one of the Hirzebruch surfaces of rank d 【less than or equal】 2. He also studied a construction of explicit self-dual neutral Khaler metrics on the product of complex projective lines.
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