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Research on geometries of Differential Systems and Parabolic geometries

Research Project

Project/Area Number 23540065
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

YAMAGUCHI Keizo  北海道大学, -, 総長 (00113639)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywords接触幾何学 / 微分式系 / 階別単純リー環 / 包合系 / 接触変換 / 単純階別リー環 / パラボリック幾何学 / 単純階別りー環
Research Abstract

We established the notion of PD-manifolds, which describes, through the concept of differentail systems, the geometry of systems of second order partial differential equations for one unknown function under contact transformations. Moerover we established two step Reduction Theorem, which is basic to Contact Geometry of Second Order.
By utilizing this Reduction Theorem, we explicitly show how to construct various classes of overdetermined systems of second order partial differential equations, for which the contact equivalence problems are reduced to that of Parabolic Geometries(i.e., the geometries associated with the simple graded Lie algebras).

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (14 results)

All 2014 2013 2012 2011 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (9 results) (of which Invited: 3 results)

  • [Journal Article] Contact Geometry of Second Order II2014

    • Author(s)
      K.Yamaguchi
    • Journal Title

      AdvancedStudies in Pure Math

      Volume: 45

    • NAID

      120006459708

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Contact Geometry of Second Order II2014

    • Author(s)
      K.Yamaguchi
    • Journal Title

      Advanced Studies in Pure Math.

      Volume: 45

    • NAID

      120006459708

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lie tensor product manifolds2012

    • Author(s)
      H.Sato and K.Yamaguchi
    • Journal Title

      Demonstratio Mathematica

      Volume: 45, No4 Pages: 909-927

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lie tensor product Manifolds2012

    • Author(s)
      Hajime Sato and Keizo Yamaguchi
    • Journal Title

      Demonstratio Mathematica

      Volume: 45, No4 Pages: 909-927

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lie temsor product manifolds2012

    • Author(s)
      Hajime Sato and Keizo Yamaguchi
    • Journal Title

      Demonstratio Mathematica

      Volume: 45

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Contact Geometry of Second Order2013

    • Author(s)
      K. Yamaguchi
    • Organizer
      Polish-Japanese Siguralities Working Days
    • Place of Presentation
      Banach Center, Warsaw
    • Year and Date
      2013-08-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Contact Geometry of Second Order2013

    • Author(s)
      K.Yamaguchi
    • Organizer
      Polish-Japanese Siguraliries Working Days
    • Place of Presentation
      Banach Center, Warsaw, Poland
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] B3-geometry in contact geometry of second order2012

    • Author(s)
      K. Yamaguchi
    • Organizer
      The Interaction of Geometry and Representation Theory, Exploring new frontiers at Erwin Schroedinger Institute
    • Place of Presentation
      Vienna
    • Year and Date
      2012-09-12
    • Related Report
      2013 Final Research Report
  • [Presentation] Contact Geometry of Second Order2011

    • Author(s)
      山口佳三
    • Organizer
      Encounter with Mathematics
    • Place of Presentation
      中央大学
    • Year and Date
      2011-10-15
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Reduction Theorems in contact geometry of second order2011

    • Author(s)
      K. Yamaguchi
    • Organizer
      The Geometry of Differential Equations
    • Place of Presentation
      Australian National University
    • Year and Date
      2011-09-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Reduction Theorems in Contact Geometry of Second Order2011

    • Author(s)
      Keizo Yamaguchi
    • Organizer
      The Geometry of differential equations(招待講演)
    • Place of Presentation
      Australian National University(Australia)
    • Related Report
      2011 Research-status Report
  • [Presentation] Contact Geometry of Second Order2011

    • Author(s)
      山口 佳三
    • Organizer
      Encounter with Mathematics(招待講演)
    • Place of Presentation
      中央大学(東京都)
    • Related Report
      2011 Research-status Report
  • [Presentation] B_3-Geometry in Contact Geometry of Second Order

    • Author(s)
      Keizo Yamaguchi
    • Organizer
      The Interaction of Geometry and Representation Theory
    • Place of Presentation
      Erwin Schrodinger Institute(オーストリア)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Reduction Theorems in Contact Geometry of Second Order

    • Author(s)
      Keizo Yamaguchi
    • Organizer
      Seminar Talk
    • Place of Presentation
      Auckland University(ニュージーランド)
    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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