Project/Area Number  08454012 
Research Category 
GrantinAid for Scientific Research (B)

Section  一般 
Research Field 
Geometry

Research Institution  Hokkaido Univ. 
Principal Investigator 
YAMAGUCHI Keizo Graduate School of Sciences, Hokkaido University, Prof., 大学院・理学研究科, 教授 (00113639)

CoInvestigator(Kenkyūbuntansha) 
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)
森吉 仁志 北海道大学, 大学院・理学研究科, 助教授 (00239708)

Project Fiscal Year 
1996 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,400,000 (Direct Cost : ¥3,400,000)
Fiscal Year 1998 : ¥1,700,000 (Direct Cost : ¥1,700,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Contact Transformation / Hypergeometric Systems / Quasilinear First Order PDE / Viscosity Solution / Integrable geodesic flow / Lagrange Stability / Hyperelliptic mopping class groups / 接触交換 / 超幾何方程式系 / 準線形二階偏微分方程式 / 超性解の分岐 / 可積分測地流 / ラフランシュ安定性 / 超楕円写像類群 / 接触変換 / 準線形一階偏微分方程式 / 接触幾何学 / 例外形単純リー環 / 二階の過剰決定系 / 二階偏微分方程式系 / 例外単純リー環 / 同値問題 / 超幾何微分方程式系 
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(k1 , n1) (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 forquasilinear first order partial differential equations and also classified the generic bifurcation of viscosity solutions for HamiltonJacobi equations of space dimension 1. Kiyohara defined the notion of Liouville manifolds and KahlerLiouville 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 socalled "Clmetrics" on the Sphere. Ishikawa showed the transversality theorem of ThomMather 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 GelfondFuchs cohomology.
