Project/Area Number 
13640084

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

Research Institution  Kagoshima University 
Principal Investigator 
AIKOU Tadashi Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (00192831)

CoInvestigator(Kenkyūbuntansha) 
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)
酒井 幸吉 鹿児島大学, 理学部, 教授 (20041759)

Project Period (FY) 
2001 – 2002

Project Status 
Completed (Fiscal Year 2002)

Budget Amount *help 
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥2,200,000 (Direct Cost: ¥2,200,000)

Keywords  Finsler metrics / Bott connections / Kahler fibrations / Projective flatness / 複素Finsler計量 / 複素Finsler接続 / 擬ケーラー計量 
Research Abstract 
In this research, we have investigated complex Bott connections and its applications to complex Finsler geometry in the period 20012002. 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)".
