1998 Fiscal Year Final Research Report Summary
Contact Geometry of Second Order
| Project/Area Number |
08454012
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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 | Hokkaido Univ. |
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Principal Investigator |
YAMAGUCHI Keizo Graduate School of Sciences, Hokkaido University, Prof., 大学院・理学研究科, 教授 (00113639)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAZUMI Nariya Graduate School of Sciences, Hokkaido University, Assoc.Prof., 大学院・理学研究科, 助教授 (30214646)
NAKAI Isao Graduate School of Sciences, Hokkaido University, Assoc.Prof., 大学院・理学研究科, 助教授 (90207704)
ISHIKAWA Goo Graduate School of Sciences, Hokkaido University, Assoc.Prof., 大学院・理学研究科, 助教授 (50176161)
KIYOHARA Kazuyoshi Graduate School of Sciences, Hokkaido University, Assoc.Prof., 大学院・理学研究科, 助教授 (80153245)
IZUMIYA Syuichi Graduate School of Sciences, Hokkaido University, Prof., 大学院・理学研究科, 教授 (80127422)
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| Project Period (FY) |
1996 – 1998
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| Keywords | Contact Transformation / Hypergeometric Systems / Quasi-linear First Order PDE / Viscosity Solution / Integrable geodesic flow / Lagrange Stability / Hyperelliptic mopping class groups |
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| Research Abstract |
The summary of Research Results is as follows. The head investigator studied the correspondence between the equivalence problem of the systems of linear differential equations of finite type (Holonomic system) and that of the projective embedding images of their fundamental solutions (projective solution). As the application of Seashi's theory for the former problem, we showed that the image of the projective solution of the Hyper geometric system E(n, k) does not lie in the Grassmannian manifold Gr(k-1 , n-1) (the image of Plucker embedding) except for E(3,6). Furthermore we discussed the generalization of E.Cartan's paper on 5 variables.
Izumiya classified the generic singularities of solution surfaces forquasi-linear first order partial differential equations and also classified the generic bifurcation of viscosity solutions for Hamilton-Jacobi equations of space dimension 1.
Kiyohara defined the notion of Liouville manifolds and Kahler-Liouville manifolds, which are two classes of riemannian manifolds whose geodesic flows are integrable and studied their structures in detail. He carried out a part of classification and found out a new family of so-called "Cl-metrics" on the Sphere.
Ishikawa showed the transversality theorem of Thom-Mather type for the space of isotropic mappings of corank 1 into symplectic manifolds and gave the characterization of Mather type or Arnold type for the Symplectic stability and Lagrange stability of the isotropic mappings.
Kawazumi developed new tools to calculate the cohomology groups over finite fields of the hyperelliptic mapping class groups and gave an overview on the study of the cohomology groups of the moduli spaces of Riemann surfaces by the complex analytic Gelfond-Fuchs cohomology.
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