2011 Fiscal Year Final Research Report
A global theory of Finsler geometry and its applications
| Project/Area Number |
21540087
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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 鹿児島大学, 理工学研究科, 教授 (00192831)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAJIMA Kimio 鹿児島大学, 大学院・理工学研究科, 教授 (40107850)
OBITSU Kunio 鹿児島大学, 大学院・理工学研究科, 准教授 (00325763)
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| Project Period (FY) |
2009 – 2011
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| Keywords | フィンスラー計量 / フィンスラー多様体 / Finsler-Kahler計量 / averaged metrics / averaged connection / Kahler fibration |
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| Research Abstract |
In this research, we have investigated Finsler geometry using the method in the geometry of fibered Riemannian manifolds. We have shown that our method is effective in the study of real or complex Finsler geometry. In particular, in this research, we have investigated conformal geometry of real Finsler manifold, and the negativity of holomorphic vector bundles over a compact complex manifold through the study of the projective bundle associated with it. Further we have obtained some new results by using the averaged metrics and connections.
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