1994 Fiscal Year Final Research Report Summary
Geometry of Manifolds and Global Analysis
| Project/Area Number |
05302002
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tohoku University |
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Principal Investigator |
NISHIKAWA Seiki Tohoku University, Faculty of Science, Professor, 理学部, 教授 (60004488)
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| Co-Investigator(Kenkyū-buntansha) |
IWAI Toshihiro Kyoto University, Faculty of Engineering, Professor, 工学部, 教授 (10021635)
KASUE Atsushi Osaka City University, Faculty of Science, Professor, 理学部, 教授 (40152657)
BANDO Shigetoshi Tohoku University, Faculty of Science, Associate Professor, 理学部, 助教授 (40165064)
FUKAYA Kenji Kyoto University, Faculty of Science, Professor, 理学部, 教授 (30165261)
OGIUE Koichi Tokyo Metropolitan University, Faculty of Science, Professor, 理学部, 教授 (10087025)
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| Project Period (FY) |
1993 – 1994
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| Keywords | Geometry of manifolds / Global analysis / Geometric variational problem / Riemannian geometry / Complex differential geometry / Dynamical system / Symplectic geometry / Integrable system |
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| Research Abstract |
The pourpose of this project is to promote cooperative researches of the Geometry of Manifolds and its related problems from the point of view of Global Analysis. To pursue the project, a working group of coordinators consisting of leading researchers in this field is organized, and the following symposiums and warkshops have been executed.
1.Symposium in Differential Geometry Two symposiums were held in 1993 and 1994 to cultivate comprehensive studies in Geomerty and Global analysis. The one in 1993 was linked with the First International Research Institute of the Mathematical Society of Japan, which was a two-week international conference, to promote international resarch cooperation. Many results have been obtained during these symposiums as well as through subsequent researches. Among them, for instance, new examples of minimal surfaces of higher genus having catenoid-type ends are constructed(by Umehara and Yamada et al.), many interactions are found between the research of harmoni
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c maps and that of nonlinear integrable systems(by Ohnita and Miyaoka et al.), the singularities, differentiable structures and Riemannian structures of Alexandrov spaces with curvature bounded below are determined(by Otsu and Shioya et al.)and multi-fold Kepler systems are discovered(by Iwai and Uwano et al.).
Workshops To promote joint researches, 11 workshops have been held on Nilpotent geometry and Analysis ; Complex differential geometry ; Dynamical system and Differential geometry ; Harmonic maps and Minimal surfaces ; Various methods in Riemannian geometry ; Homogeneous spaces and Variational problems ; Harmonic maps, Integrable systems and Moduli spaces ; Geometry of Riemannian manifolds and conformal structures ; Global analysis and Geometry. Also, to encourage graduate students and young researchers a workshop for surveys in symplectic geometry was carried out.
To collect worldwide up-to-date research results and preprints in the field of Geometry of manifolds and Global analysis and make them easily accessible, a data base system running on email networks has been constituted for real-time public service. Less
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