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A construction of surfaces in spaces of constant curvature via integrable system method

Research Project

Project/Area Number 20740045
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionHirosaki University

Principal Investigator

KOBAYASHI Sinpei  弘前大学, 大学院・理工学研究科, 准教授 (40408654)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords平均曲率一定曲面 / ループ群 / 可積分系 / 線形常微分方程式 / 線形常微分 / 線型常微分方程式
Research Abstract

We defined complex constant mean curvature surfaces by a natural generalization of constant mean curvature surfaces in Euclidean three space and classified real form surfaces, such as constant mean curvature or constant Gauss curvature surfaces in spaces of constant curvature, for a complex constant mean curvature surface. We also characterized equivariant harmonic maps in complex projective spaces via potentials, which are matrix valued 1-forms. Moreover, a construction method of equivariant harmonic maps in complex projective spaces has been obtained from the potentials.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (22 results)

All 2011 2010 2009 2008 Other

All Journal Article (7 results) (of which Peer Reviewed: 2 results) Presentation (11 results) Remarks (4 results)

  • [Journal Article] Real forms of complex surfaces of constant mean curvature2011

    • Author(s)
      Shimpei Kobayashi
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 363 Pages: 1765-1788

    • Related Report
      2010 Final Research Report
  • [Journal Article] Totally symmetric surfaces of constant mean curvature in hyperbolic 3-space2010

    • Author(s)
      Shimpei Kobayashi
    • Journal Title

      Bulletin of the Australian Mathematical Society

      Volume: 82 Pages: 240-253

    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Journal Article] Complex surfaces of constant mean curvature fibered by minimal surfaces2010

    • Author(s)
      Josef Dorfmeister, Shimpei Kobayashi, Franz Pedit
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 39 Pages: 1-55

    • Related Report
      2010 Final Research Report
  • [Journal Article] Complex surfaces of constant mean curvature fibered by minimal surfaces2010

    • Author(s)
      Josef Dorfineister, Shimpei Kobayashi, Franz Pedit
    • Journal Title

      Hokkaido Mathematical Journal 39

      Pages: 1-55

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Note on equivariant harmonic maps in complex projective spaces2009

    • Author(s)
      Shimpei Kobayashi
    • Journal Title

      Annals of Global Analysis and Geometry

      Volume: 36 Pages: 375-380

    • Related Report
      2010 Final Research Report
  • [Journal Article] Note on equivariant harmonic maps in complex projective spaces2009

    • Author(s)
      Shimpei Kobayashi
    • Journal Title

      Annals of Global Analysis and Geometry 36

      Pages: 375-380

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Constant mean curvature surfaces in hyperbolic 3-space via loop groups

    • Author(s)
      Josef Dorfmeister, Jun-ichi Inoguchi, Shimpei Kobayashi
    • Journal Title

      Journal fur die reine und angewandte Mathematik

      Volume: (印刷中)

    • Related Report
      2010 Final Research Report
  • [Presentation] Constant Gauss Curvature Cylinders2010

    • Author(s)
      小林真平
    • Organizer
      Submanifold Geometry and Lie Group Actions
    • Place of Presentation
      東京理科大学
    • Year and Date
      2010-09-09
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Dressing action on complex CMC surfaces and real forms2010

    • Author(s)
      Shimpei Kobayashi
    • Organizer
      Oberseminar Differentialgeometrie
    • Place of Presentation
      Universitat Augsburg
    • Year and Date
      2010-07-02
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Constant mean curvature surfaces in H^3 via integrable system methods2010

    • Author(s)
      Shimpei Kobayashi
    • Organizer
      Progress in Surface Theory
    • Place of Presentation
      Oberwolfach Mathematical Institute
    • Year and Date
      2010-05-06
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Global solutions of elliptic (G, rho)-systems2009

    • Author(s)
      小林真平
    • Organizer
      New aspects of surface theory
    • Place of Presentation
      東京都立大学
    • Year and Date
      2009-05-15
    • Related Report
      2010 Final Research Report
  • [Presentation] Global solutions of elliptic(G, rho)-systems2009

    • Author(s)
      小林真平
    • Organizer
      New aspects of surface theory
    • Place of Presentation
      東京都立大学
    • Year and Date
      2009-05-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] Survey of integrable surfaces2009

    • Author(s)
      小林真平
    • Organizer
      GEOSOCK Seminar
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2009-05-13
    • Related Report
      2010 Final Research Report
  • [Presentation] Surveys of integrable surfaces2009

    • Author(s)
      小林真平
    • Organizer
      GEOSOCK seminar
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2009-05-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] Harmonic trinoids in complex projective spaces2009

    • Author(s)
      小林真平
    • Organizer
      Fusion of Integrable Systems and Geometry
    • Place of Presentation
      東北大学
    • Year and Date
      2009-04-19
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 複素平均曲率一定曲面と実形2009

    • Author(s)
      小林真平
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] Harmonic trinoids in complex projective spaces, Integrable systems2008

    • Author(s)
      Shimpei Kobayashi
    • Organizer
      Geometry and Visualization 2008
    • Place of Presentation
      九州大学
    • Year and Date
      2008-12-12
    • Related Report
      2010 Final Research Report
  • [Presentation] Harmonic trinoids in complex projective spaces2008

    • Author(s)
      小林真平
    • Organizer
      Integrable systems, Geometry and Visualization 2008
    • Place of Presentation
      九州大学
    • Year and Date
      2008-12-12
    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.st.hirosaki-u.ac.jp/~shimpei

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.st.hirosaki-u.ac.jp/~shimpei

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.st.hirosaki-u.ac.jp/~shimpei

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.st.hirosaki-u.ac.jp/-shimpei/

    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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