• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Contact Geometry of Second Order

Research Project

Project/Area Number 08454012
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHokkaido Univ.

Principal Investigator

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

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)
森吉 仁志  北海道大学, 大学院・理学研究科, 助教授 (00239708)
Project Period (FY) 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)
KeywordsContact Transformation / Hypergeometric Systems / Quasi-linear First Order PDE / Viscosity Solution / Integrable geodesic flow / Lagrange Stability / Hyperelliptic mopping class groups / 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(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.

Report

(4 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] K.Yamaguchi: "On the Rigidity of Differential Systems modelled on Hermitian Symmetric Spaces and Disproofs of a Conjecture concerning Modularlnterpretations of Configuration Spaces" Advanced Studies in Pure Math.25. 25. 318-354 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Izumiya: "A normal form of first order partial differential equation with singular solution" Tokyo Journal of Mathematics. 18. 485-488 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Izumiya: "Singularities of solution surfaces of quasilinear first order P.D.E." Geometriae Dedicata. 64. 331-341 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Kiyohara: "Two classes of Riemannian manifolds whose geodesic flows are integrable" Memoirs of AMS. 130/619. 1-143 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Ishikawa: "Symplectic and Lagrange stabilities of open Whitney umbrellas" Invent.Math.126-2. 215-234 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Kawazumi: "Homology of hyperelliptic mapping class groups for surfaces" Topology and its appl.76. 203-216 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 泉屋周一: "行列と連立一次方程式" 共立出版, 118 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 石川剛郎: "線形写像と固有値" 共立出版, 136 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Yamaguchi, T.Sasaki and M.Yoshida: "On the Rigty of Differential Systems modelled on Hermitian Symmetric Spaces and Disproofs of a Conjecture concerning Modular Interpretations of Configuration Spaces." Advanced Studies in Pure Math.25 (CR-Geometry and Overdetermined Systems). 25. 318-354 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Izumiya: "A normal form of first order partial differential equations with singular solution." Tokyo Journal of Mathematics. Vol.18. 485-488 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Izumiya and W-Z.Sun: "Singularities of solution surfaces of quasilinear first order partial differential equations." Geometriae Dedicata. Vol.64. 331-341 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Kiyohara: "Two classes of Riemannian manifolds whose geodesic flows are integrable." Memoirs of AMS.130/619. 1-143 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Ishikawa: "Symplectic and Lagrange stabilities of open Whitney umbrellas." Invent.math.Vol.126-2. 215-234 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Kawazumi: "Homology of hyperelliptic mapping class groups for surfaces." Topology and its appl.76. 203-216 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Izumiya, Ishikawa etal.: Matrix and Systems of linear equations. Kyouritu Shuppan, 1-118 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Ishikawa, Izumiya etal.: Linear map and Eigenvalues. Kyouritu Shuppan, 1-136 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.YAMAGUCHI: "G_2-Geometry of Orerdetermined System of Second Order" Progress in Mathimatics(Birkhaim). 180. 52-75 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.IZUMIYA: "Characteristic vector fild for form order pertial differential equation" Journal of Nonlinia Analysis,theory method and applotin. 32. 575-582 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] G.Ishikawa: "A relative transversilts theorem and its applications" Pitman Research Nots in Meitl. 381. 84-93 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Izumiya: "Geometric Singularitus for solution of single conservation laws" Archive for Rational Mechanics and Analysis. 139. 255-290 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] G.Ishikawa: "A criterion for finite topological deteroinacy of smooth map-germs" Proc.London Math. Soc.74・3. 662-700 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Kawazumi: "Honology of hyperelliptic mapping class groups for surgaces" Topology and its application. 76. 203-216 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Kiyohara: "Two classes of Riemannian manifolds whose geodesic flow are integrall" Memoirs of A.M.S.130/169. 1-143 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Yamaguchi: "On the Rigidity of Differential Systems modelled on Hermition symmetion speces and Disproofs of a conyicture concerning Modular Interpretation of Configuration Speces" Advanced Studies in Pure Math.25. 318-354 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 佐々木 武: "On the Rigidity of Differential Systems modelled on Hermtian Symmetric Spaces" Advanced Studies in Pure Mathematics. 25. 318-354 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 清原一吉: "Two classes friemannian manifolds whose geodesu-flows are integrable" Memoirs of the AMS. (in press). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 中居 功: "The classification of curvilinear angles in the complex plane and the groups of Ihclomorphic diffeomorphisms" Annals Math.Toulouse. (in press). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 泉屋周一: "Formation of singularities for riscosity solutions of Hamilton-Jacobi equation" Banach Centes Publication. 33. 127-148 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 石川剛郎: "Symplectic and Lagrangian stability of open whitney umbrellas" Invent Math.126・2. 215-234 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 森吉仁志: "The Godbillon-Veg cyelic cocycle. and longitudinal Dirae operators" Pacific J.of Math.172・2. 483-539 (1996)

    • Related Report
      1996 Annual Research Report

URL: 

Published: 1997-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi