2004 Fiscal Year Final Research Report Summary
The study of differential geometry of Kahler-fibrations and its applications.
| Project/Area Number |
15540084
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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 |
Geometry
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| Research Institution | Kagoshima University |
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Principal Investigator |
AIKOU Tadashi Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (00192831)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAJIMA Kimio Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (40107850)
OBITSU Kunio Kagoshima University, Faculty of Science, Associate Professor, 理学部, 助教授 (00325763)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Kahler fibration / Finsler metrics / Chern-Finsler connections / Projective flatness / Projective bundles |
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| Research Abstract |
In this research, we have investigated the complex differential geometry of Kahler fibrations and its applications in the term 2003-2004. In particular, we have constructed the fundamental research of Kahler fibrations to apply it to complex Finsler geometry. The main subjects of this project are (1)the study of Kahler fibartion with isometric fibres, (2)the study of Kahler metric on a minimal ruled surface over a compact Riemann surface.
The main content of this research is the investigation of connections on the total space of the fibration, which is naturally related to the theory of Finsler connections. In particular, in the case where the space is a minimal ruled surafce P(E) over a compact Riemann surface, we have obtained some results on Kahler metrics of contant scalr curvature. Especially we have investigated the projective flatness of the bundle E. Moreover, since the projective flatness and the stability of bundles are equivalent in this case, we have obtained some relations between the existence of Kahler metrics of constant scalar curvature and the stability of the bundle E under the some assumptions.
The head investigator have reported some results in this project at the international conference held at Debrecen(Hungary,1003), Tianjin(China,2004) and Natsushima(Sendai, Japan,2004), and he is preparing a paper entitled "On the Chenr-Finsler connection on complex Finsler bundles" for publishing.
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Research Products
(13 results)
