2002 Fiscal Year Final Research Report Summary
The study of Bott connection and its applications to Finsler geometry
| Project/Area Number |
13640084
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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) |
NISHIDA Kotoba Kagoshima University, Faculty of Science, Research Associate, 理学部, 助手 (10274838)
OHMOTO Toru Kagoshima University, Faculty of Science, Associate Professor, 理学部, 助教授 (20264400)
MIYAJIMA Kimio Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (40107850)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Finsler metrics / Bott connections / Kahler fibrations / Projective flatness |
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| Research Abstract |
In this research, we have investigated complex Bott connections and its applications to complex Finsler geometry in the period 2001-2002. In 2001, we have mainly studied some relations between the complex Bott connections and complex Finsler connections. Under the results obtained in 2001, we have studied the flatness and projective flatness of complex Finsler metrics, and moreover, the differential geometry of Kahler fibrations with pseudo Kahler metrics in 2002.
The main contents of this research is the investigation of complex Finsler connection which is introduced on the relative tangent bundle over the projective bundle. In terms of this connection, we can investigate the projective flatness of complex Finsler metrics, and finally we obtained the projective curvature which is the obstruction of projective flatness. Such an investigation leads us naturally to the study of minimal ruled surface over a compact Riemann surface. In fact, the Kahler metric on such a surface induces a complex Finsler metric with negative curvature in the corresponding vector bundle. The basic and important fact is that the projective flatness of the corresponding Finsler metric is equivalent to that the minimal ruled surface is the total space of a Kahler submersion with isometric fibers to the base Riemann surface.
The main results in this research are contained in "Kahler fibrations and complex Finsler geometry (preprint, 2002)" and "A note on some special Finsler manifold (preprint, 2002)".
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