2001 Fiscal Year Final Research Report Summary
Projective contact geometry and singularity theory
| Project/Area Number |
10440013
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | HOKKAIDOUNIVERSITY |
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Principal Investigator |
ISHIKAWA Goo Hokkaido University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (50176161)
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| Co-Investigator(Kenkyū-buntansha) |
SUWA Tatsuo Hokkaido University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (40109418)
YAMAGUCHI Keizo Hokkaido University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (00113639)
IZUMIYA Shyuichi Hokkaido University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (80127422)
KIYOHARA Kazuyoshi Hokkaido University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (80153245)
ONO Kaoru Hokkaido University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (20204232)
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| Project Period (FY) |
1998 – 2001
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| Keywords | simple singularity / symplectic defect / contact geometry / Grassmannian geometry / Monge-Ampere equation / Gauss mapping / dual variety / developable submanifold |
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| Research Abstract |
We have organized the joint works: The head investigator and the investigator Toru Morimoto (see the references); the head investigator and the investigators Reiko Miyabka and Makoto Kimura (submitted); the head Investigator and Ilya Bogaevski(see the references); the head investigator and S. Janeczko (submitted); the head investigator and V. Zakalyukin; and several other projects with investigators. For instance, we have the following result: The isotropic bifurcation problem is reduced to the classification of varieties by symplectomorphisms in the reduced space. The complete symplectic classification of Bruce-Gaffhey's plane curve singularites is provided and is applied to obtain naturally the Lagrangian openings. Moreover we study the Monge-Ampere equations from the view points of contact geometry and investigate the global structure and singularities of Monge-Ampere equations. Also we have the results on the singularities of Gauss mappings and dual varieties, appearing in the com formal geometry and Grassmannian geometry and application to differential equations. We construct developable submanifolds by using minimal submanifolds, harmonic mappings and calibrations.
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