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- Material Type
- 文書・図像類
- Author/Editor
- 愛甲, 正
- Author Heading
- Publication, Distribution, etc.
- Alternative Title
- A global theory of Finsler geometry and its applications
- Text Language Code
- jpn
- Target Audience
- 一般
- Note (General)
- 2009-2011年度科学研究費助成事業(科学研究費補助金(基盤研究(C)))研究成果報告書 課題番号：21540087 研究代表者：愛甲正 (鹿児島大学大学院理工学研究科(理学系)教授)本研究では，フィンスラー幾何学をfibered Riemannian多様体の微分幾何学の観点から研究した。特に，実及び複素フィンスラー幾何学に関しては，この手法が有効な研究手法であることを示した。特に，本研究では実フィンスラー多様体の共形幾何学や，複素多様体上の正則ベクトル束の負性について, その射影化束の微分幾何学をフィンスラー幾何学とみなす事により研究した。更に，計量や接続の平均化という手法により，新しい結果を得た．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.