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A geometric study of invariants of the system of differential equations of finite type.

Research Project

Project/Area Number 15540055
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHokkaido University of education

Principal Investigator

YATSUI Tomoaki  Hokkaido University of Education, Faculty of education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (00261371)

Co-Investigator(Kenkyū-buntansha) FUKUI Masaki  Hokkaido University of Education, Faculty of education, Asahikawa, Professor, 教育学部・旭川校, 教授 (20002628)
OKUYAMA Teturo  Hokkaido University of Education, Faculty of education, Asahikawa, Professor, 教育学部・旭川校, 教授 (60128733)
ABE Osamu  Hokkaido University of Education, Faculty of education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (30202659)
KOMURO Naoto  Hokkaido University of Education, Faculty of education, Asahikawa, Assistant Professor, 教育学部・旭川校, 助教授 (30195862)
KITAYAMA Masashi  Hokkaido University of Education, Faculty of education, Kushiro, Professor, 教育学部・釧路校, 教授 (80169888)
Project Period (FY) 2003 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsCartan connecton / Invariants / diffferential equation
Research Abstract

In this project, we reserched the geometric invariants of the system of differential equtations of finite type. The system (Χ) of (k+1)-th order holonomic differential equations of integrable type defines an open submanifold R of k-jet space j^k and a differential system E on R. The symbol algebra of the pseudo-projective structure of order k+1 bidegree (m+1,1) of (R ; E,F) on R associated with (Χ) is a pseudo-projective fundamental graded Lie algebra of order k+1 of bidegree (n,r). N.Tanaka showed that there is naturally a normal Cartan connection (P,ω) of type G/G^<(0)> associated with E. Moreover the harmonic part HK of the curvature function K of (P,ω) generates the fundamental invariants of the Cartanconnection (P,ω), which takes values in the second generalized Spencer cohomology space H^2(δ). Therefore we need to investigate the space H^2(δ). We first obtained the non-vanishing subspaces of the generalized Spencer cohomology space H^2(δ) of pseudo-projective graded Lie algebras. B.Doubrov showed that the curvature function HK of the Cartan connection takes values in the subspace F^1H^2(δ) of H^2(δ). We otained the generators of subspaces F^1H^2(δ) in case δ is a pseudo-projectiv graded Lie algebra of order k+1 of bidegree (m+1,1).

Report

(3 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • Research Products

    (18 results)

All 2004 2003 Other

All Journal Article (13 results) Publications (5 results)

  • [Journal Article] Domination property of the set of upper bound in ordered linear spaces2004

    • Author(s)
      N.Komuro
    • Journal Title

      Proc.of International Conference of Nonliear Analysis and Convex Analysis (Yokohama Publ.)

      Pages: 217-226

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Homogeneous system of parameters for cohomology algebras of finite groups2004

    • Author(s)
      T.Okuyama, H.Sasaki
    • Journal Title

      Archiv der Mathematik 82

      Pages: 110-121

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Homogeneous system of parameters for cohomology algebras of finite groups2004

    • Author(s)
      T.Okuyama, H.Sasaki
    • Journal Title

      Archiv der Mathematik 2

      Pages: 110-121

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Domination property of the set of upper bound in ordered linear spaces2004

    • Author(s)
      N.Komuro
    • Journal Title

      Proc.of International Conference of Nonliear Analysis and Convex Analysis (Yokohama Publsihers.)

      Pages: 217-226

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Randers spaces of constant flag curvature induced by almost contact metric structures2004

    • Author(s)
      I.Hasegawa, V.S.Sabau, H.Shimada
    • Journal Title

      Hokkaido Mathematical Journal 33-1

      Pages: 215-232

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Domination property of the set of upper bound in ordered linear spaces2004

    • Author(s)
      N.Komuro
    • Journal Title

      Proc. of International Conference of Nonlinear Analysis and Convex Analysis (Yokohama Publishers.)

      Pages: 217-226

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Induced vector fields in a hypersurface of Riemannian tangent bundle2003

    • Author(s)
      M.Kitayama
    • Journal Title

      Finsler and Lagrane geometries (Kluwer Acad.Publ.)

      Pages: 109-111

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] The set of upper bound in ordered linear spaces2003

    • Author(s)
      N.Komuro
    • Journal Title

      Proc.of International Conference of Nonliear Analysis and Convex Analysis (Yokohama Publ.)

      Pages: 197-207

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Mass formula for two-dimensional flavor non-siglet masons2003

    • Author(s)
      O.Abe, N.Watanabe
    • Journal Title

      The European Physical Journal C30

      Pages: 513-516

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] The a-invariant and Gorensteiness of graded rings associated to filtrations of ideals in regular local rings2003

    • Author(s)
      S.Sato, F.Hayama, S-i.Iai
    • Journal Title

      Proc.Amer.Math.Soc. 131

      Pages: 87-94

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On some relations of Finsler hypersurface2003

    • Author(s)
      M.Kitayama
    • Journal Title

      Tenser N.S. 64 1

      Pages: 81-11

    • NAID

      10012827605

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] The a-invariant and Gorensteiness of graded rings associated to filtrations of ideals in regular local rings2003

    • Author(s)
      Sato, F.Hayama, S-i.Iai
    • Journal Title

      Proc.Amer.Math.Soc. 131

      Pages: 87-94

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Contact CR-warped product submanifolds in Sasakian manifolds2003

    • Author(s)
      I.Hasegawa, I.Mahai
    • Journal Title

      Geom.Dedica 102

      Pages: 143-150

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] M.Kitayama: "Induced vector fileds in a hypersurface of Riemannian tangent bundle"Finsler and Lagrane geometries (Kluwer Acad.Publ.). 109-111 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Komuro: "The set of upper bound in order linear spaces"Proc.of international Conference of Nonliear Analysis and Convex Analysis(Yokohama Publ.). (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] O.Abe, N.Watanabe: "Mass formula for two-dimensional flavor non-siglet masons"The European Physical Journal. C30. 513-516 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Sato, F.Hayama, S-i.Iai: "The a-invariant and Gorensteiness of graded rings associated to filtrations of ideals in regular local rings"Proc.Amer.Math.Soc.. 131. 87-94 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Okuyama, H.Sasaki: "Homogeneous system of parameters for cohomology algebras of finite groups"Archiv der Mathematik. (掲載予定).

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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