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GEOMETRY THEORY OF SYSTEMS OF ORDINARY DEFFERENTIAL EQUATIONS

Research Project

Project/Area Number 62540001
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionDEPARTMENT OF MATHEMATICS, HOKKAIDO UNIVERSITY

Principal Investigator

TANAKA Noboru  HOKKAIDO UNIVERSITY Fac, of Science, 理学部, 教授 (80025296)

Co-Investigator(Kenkyū-buntansha) SUWA Tatsuo  HOKKAIDO UNIVERSITY Fac, of Science, 理学部, 教授 (40109418)
IZUMIYA Shyuichi  HOKKAIDO UNIVERSITY Fac, of Science, 理学部, 助教授 (80127422)
KIYOHARA Kazuyoshi  HOKKAIDO UNIVERSITY Fac, of Science, 理学部, 助手 (80153245)
YAMAGUCHI Keizo  HOKKAIDO UNIVERSITY Fac, of Science, 理学部, 助教授 (00113639)
MORIMOTO Tohru  HOKKAIDO UNIVERSITY Fac, of Science, 理学部, 助教授 (80025460)
Project Period (FY) 1987 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1988: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1987: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsSYSTEM OF ORDINARY DIFFERENTIAL EQUATION / INVARIANT / CARTAN CONNECTION / AUTOMORPHISM GROUP / 不変量 / 幾何構造
Research Abstract

1. THE HEAD INVESTIGATOR STUDIED THE GEOMETRY OFPSEUDO-PROJECTIVE SYSTEMS OF ORDER K( 2), WHICH FORMULATES THE GEOMETRY OF A CERTAIN CLASS OF INVOLUTIVE SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS OF ORDER K. NOTE THAT THIS CLASS INCLUDES THE CLASS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS OF ORDER K.
(1) FIRST OF ALL HE DETERMINDE THE MODEL SYMBOL ALGEBRA L OF PSEUDO-PROJECTIVE SYSTEM OF ORDER K, AND CALCULATED ITS PROLONGATION G.
(2) THEN HE SHOWED THTA THERE IS NATURALLY ASSOCIATED TO EVERY PSEUDO-PROJECTIVE SYSTEM R OF ORDER K A NORMAL CARTAN CONNECTION OF MODEL SPACE G/G^<(0)>, WHERE G/G^<(0)> IS NATURALLY CONSTRUCTED FROM G.
(3) FURTHERMORE HE STUDIED THE STANDARD PSEUDO-PROJECTIVE SYSTEM R_O OF ORDER K IN DETAIL, AND CHARACTERIZED IT IN TERMS OF THE PROJECTIVE GEOMETRY.
2. THE HEAD INVESTIGATOR ALSO GAVE A RIGOROUS FORMULATION AS WELL AS PROOF OF LIE-CARTAN'S INTEGRATION THEORY FOR COMPLETELY INTEGRABLE SYSTEMS. AMONG OTHERS LET BE A CARTAN SYSTEM, WHICH MEANS A TRANSVERSE ABSOLUTE PARALLELISM ON A MANIFOLD P WITH A COMPLETELY INTEGRABLE SYSTEM E. LET g() DENOTE THE REDUCED LIE ALGEBRA OF INFINITESIMAL AUTOMORPHISMS OF . THEN HE RIGOROUSLY PROVED THE FOLLOWING THEOREM DUE TO ELIE CARTAN: THE INTEGRATION OF E CAN BE CARRIED OUT BY QUADRACTURES AND THE INTEGRATIONS OF LIE'S DIFFERENTIAL EQUATINS ASSOCIATED WITH THE SIMPLE COMPONENTS OF g( ).

Report

(3 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • 1987 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] 森本徹: Hokkaido Math.J.17. 45-81 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 清原一吉: Japanese J.Math.13. 209-234 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 泉屋周一: Proc.Amer.Math.Soc.101. 748-752 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 泉屋周一: Hokkaido Math.J.16. 201-206 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 諏訪立雄: Proc.Amer.Math.Soc.104. 131-134 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 諏訪立雄: J.Diff.Geom.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 諏訪立雄: Bull.London Math.Soc.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 中村郁: J.Math.Soc.Japan. 39. 521-535 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 中村郁: Algebraic Geom.Comm.Algebra. 379-404 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] TOHRU MORIMOTO: "TRANSITIVE LIE ALGEBRAS ADMITTING DIFFERENTIAL SYSTEMS" HOKKAIDO MATH. J.17. 45-81 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] KAZUYOSHI KIYOHARA: "RIEMANNIAN METRICS WITH PERIODIC GEODESIC FLOWS ON PROJECTIVE SPACES" JAPANESE J. MATH.13. 209-234 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SHYUICHI IZUMIYA: "ON LEGENDRIAN SINGULARITIES" PROC. AMER. MATH. SOC.101. 748-752 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SHYUICHI IZUMIYA: "LOCAL TOPOLOGICAL MODELS OF ENVELOPS" HOKKAIDO MATH. J.16. 201-206 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] TATSUO SUWA: "A FACTORIZATION THEOREM FOR UNFOLDINGS OF ANALYTIC FUNCTIONS" PROC. AMER. MATH. SOC.104. 131-134 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] TATSUO SUWA: "D-MODULES ASSOCIATED TO COMPLEX ANALYTIC SINGULAR FOLIATION (TO APPEAR)" J. DIFF. GEOM.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] TATSUO SUWA: "STRUCTURE OF TJE SINGULAR SET OF A COMPLEX ANALYTIC FOLIATION" BULL. LONDON MATH. SOC. (TO APPEAR).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] IKU NAKAMURA: "MOISHEZON THREEFOLD HOMEOMORPHIC TO A P^3" J. MATH. SOC. JAPAN. 39. 521-535 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] IKU NAKAMURA: "THREEFOLDS HOMEOMORPHIC TO A HYPERQUADRIC IN P^4" ALGEBRAIC GEOM. COMM. ALGEBRA. 379-404 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] IKU NAKAMURA: "A CHARACTERIZATION OF THE PROJECTIVE SPACE (IN PREPARATION)"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 森本徹: Hokkaido Math.J.17. 45-81 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 諏訪立雄: Prof.Amer.Math.Soc.104. 131-134 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 諏訪立雄: Bull.London Math.Soc.

    • Related Report
      1988 Annual Research Report
  • [Publications] 諏訪立雄: J.Diff.Geom.

    • Related Report
      1988 Annual Research Report

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Published: 1987-04-01   Modified: 2016-04-21  

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