1992 Fiscal Year Final Research Report Summary
Study on global structures of manifolds.
| Project/Area Number |
03640048
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
IMANISHI Hideki Kyoto Univ.,Integrated Human Studies,Professor, 総合人間学部, 教授 (90025411)
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| Co-Investigator(Kenkyū-buntansha) |
GYOJO Akihiko Kyoto Univ.,Integrated Human Studies,Assistant Professor, 助教授 (50116026)
HATA Masayoshi Kyoto Univ.,Integrated Human Studies,Assistant Professor, 助教授 (40156336)
FUJIKI Akira Kyoto Univ.,Graduate School of Human&Environment Studies,Assist.Professor, 教授 (80027383)
TANDAI Kouichi Kyoto Univ.,Integrated Human Studies,Professor, 総合人間学部, 教授 (90026732)
TAKEUCHI Akira Kyoto Univ.,Integrated Human Studies,Professor, 総合人間学部, 教授 (40026761)
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| Project Period (FY) |
1991 – 1992
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| Keywords | Grassmann manifold / invriant differential operator / Kahler manifold / Einstein-Kahler metric / Dolbeault lemma / Diophantine approximation |
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| Research Abstract |
Here we summarize some of our published results listed below. [1],[2]: Let M be the Grassmann manifold of real or complex two planes respectively. A set of generators of the ring of invariant differential operators on M is determined and the eigenspace decompositions are obtained. [3]: A necessary and sufficient condition for the existence of an extremal Kahler metric on some ruled manifolds is obtained and some interesting relations between the problems of existence and uniqueness of the metric are observed. [4]: The L^2-Dolbeault lemma is established for holomorphic Hermitian vector bundles on pseudo projective manifolds. The lemma is applied to the problems of deformation of locally bounded symmetric domains and to the problem of existence of Kahler-Einstein metrics. [5],[6]: Here the problem of rational approximations of some irrational numbers are considered. This research is based on highly acculate numerical experiences which is developed through the authors research on dynamical systems.
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