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Moduli spaces of vector bundles and a generalization of harmonic maps

Research Project

Project/Area Number 20540081
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKyushu University

Principal Investigator

NAGATOMO Yasuyuki  Kyushu University, 数理学研究院, 准教授 (10266075)

Co-Investigator(Renkei-kenkyūsha) TAKAHASHI Masarou  久留米工業高等専門学校, 一般科目理科系, 准教授 (70311107)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords微分幾何 / モジュライ空間 / ベクトル束 / 調和写像 / 表現論 / 反自己双対接続 / リー群 / 対称空間 / 等径関数 / 極小部分多様体
Research Abstract

Using a characterization of harmonic maps into Grassmannians by linear equations, we construct isoparametric functions on symmetric spaces. Moreover, these are transformed into isoparametric functions on spheres by Radon transform. We describe a moduli space of harmonic maps between complex projective spaces with constant energy densities by linear algebraic datum. We also describe a moduli spaces of holomorphic maps from Hermitian symmetric spaces into complex Grassmannian manifolds in a similar method.

Report

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

    (40 results)

All 2011 2010 2009 2008 Other

All Journal Article (9 results) (of which Peer Reviewed: 8 results) Presentation (31 results)

  • [Journal Article] Harmonic maps into Grassmannians and a generalization of do Carmo-Wallach theorem, Proceedings of the 16th OCU International Academic Symposium 20082010

    • Author(s)
      長友康行
    • Journal Title

      Riemann Surfaces, Harmonic Maps and Visualization(OCAMI Studies) 3

      Pages: 41-52

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on the topology and geometry of F_4I2010

    • Author(s)
      Rafael Herrera, Yasuyuki Nagatomo
    • Journal Title

      Rendiconti di Matematica e sue Applicazioni 30

      Pages: 183-193

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Harmonic maps into Grassmannians and a generalization of do Carmo-Wallach theorem2010

    • Author(s)
      Yasuyuki Nagatomo
    • Journal Title

      Proceedings of the 16th OCU International Academic Symposium 2008

      Pages: 41-52

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on the topology and geometry of F_4I2010

    • Author(s)
      Rafael Herrera, Yasuyuki Nagatomo
    • Journal Title

      Rendiconti di Matematicae, Serie VII

      Volume: 30 Pages: 183-193

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] グラスマン多様体内の全測地的部分多様体2009

    • Author(s)
      長友康行
    • Journal Title

      数理解析研究所講究録 1668

      Pages: 1-6

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Journal Article] Twistor sections on the Wolf spaces2008

    • Author(s)
      長友康行
    • Journal Title

      Transactions of the American Mathematical Society 360

      Pages: 4497-4517

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Twistor sections on the Wolf spaces2008

    • Author(s)
      Yasuyuki Nagatomo
    • Journal Title

      Transactions of the A. M. S. 360

      Pages: 4497-4517

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Harmonic maps into Grassmannians and a generalization of de Carmo-Wallach theorem

    • Author(s)
      長友康行
    • Journal Title

      Proceedings of the 16^<th> OCU International Academic Symposium 2008 (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on the topology and geometry of F4I

    • Author(s)
      Rafael Herrera, Yasuyuki Nagatomo
    • Journal Title

      Rendiconti di Matematicae sue Applicazioni (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 複素射影直線から複素射影空間への調和写像に関する剛性定理(板東-大仁田の結果)の別証明2011

    • Author(s)
      長友康行
    • Organizer
      日本数学会 幾何学分科会
    • Place of Presentation
      早稲田大学(一般講演)
    • Year and Date
      2011-03-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2011

    • Author(s)
      長友康行
    • Organizer
      名城大学研究集会
    • Place of Presentation
      名城大学
    • Year and Date
      2011-03-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] 複素射影直線から複素射影空間への調和写像に関する剛性定理(板東-大仁田の結果)の別証明2011

    • Author(s)
      長友康行
    • Organizer
      日本数学会 幾何学分科会 一般講演
    • Place of Presentation
      早稲田大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Harmonic maps into Grassmannians and its applications to isoparametric functions and moduli problems2011

    • Author(s)
      長友康行
    • Organizer
      3rd OCAMI-TIMS workshop
    • Place of Presentation
      大阪市立大学
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行
    • Organizer
      松江微分幾何学研究集会2010
    • Place of Presentation
      島根大学
    • Year and Date
      2010-12-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行
    • Organizer
      第15回湯沢研究会
    • Place of Presentation
      湯沢グランドホテル(新潟県)
    • Year and Date
      2010-11-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] Holomorphic maps from Hermitian symmetric spaces into Grassmannians2010

    • Author(s)
      Yasuyuki Nagatomo
    • Organizer
      Lie Transformation Groups and Complex Geometry
    • Place of Presentation
      NASPAニューオータニ、越後湯沢(新潟県)
    • Year and Date
      2010-09-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行
    • Organizer
      部分多様体幾何とリー群作用2010
    • Place of Presentation
      東京理科大学 森戸記念館
    • Year and Date
      2010-09-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行
    • Organizer
      第57回幾何学シンポジウム
    • Place of Presentation
      神戸大学(基調講演)
    • Year and Date
      2010-08-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行, 高橋正郎
    • Organizer
      日本数学会幾何学分科会一般講演
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Vector bundles, isoparametric functions and Radon transforms on symmetric spaces2010

    • Author(s)
      長友康行
    • Organizer
      A.C, Mexico, Seminario de Geometr\'ia Diferencial
    • Place of Presentation
      Centro de Investigaci\'on en Matem\'aticas
    • Year and Date
      2010-03-04
    • Related Report
      2010 Final Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行
    • Organizer
      第15回湯沢研究会
    • Place of Presentation
      湯沢グランドホテル
    • Related Report
      2010 Final Research Report
  • [Presentation] Holomorphic maps from Hermitian symmetric spaces into Grassmannians2010

    • Author(s)
      長友康行
    • Organizer
      Lie Transformation Groups and Complex Geometry
    • Place of Presentation
      NASPA ニューオータニ、越後湯沢
    • Related Report
      2010 Final Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行
    • Organizer
      部分多様体幾何とリー群作用
    • Place of Presentation
      東京理科大学森戸記念館
    • Related Report
      2010 Final Research Report
  • [Presentation] Vector bundles, isoparametric functions and Radon transforms on symmetric spaces2010

    • Author(s)
      長友康行
    • Organizer
      Workshop on Hypersurfaces Geometry and Integrable Systems
    • Place of Presentation
      東北大学
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行
    • Organizer
      第57回幾何学シンポジウム 基調講演
    • Place of Presentation
      神戸大学
    • Related Report
      2010 Final Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2010

    • Author(s)
      長友康行、高橋正郎
    • Organizer
      日本数学会 幾何学分科会 一般講演
    • Place of Presentation
      慶応義塾大学
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体内の全測地的部分多様体2009

    • Author(s)
      長友康行
    • Organizer
      日本数学会幾何学分科会一般講演
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] グラスマン多様体への調和写像2009

    • Author(s)
      長友 康行
    • Organizer
      日本数学会幾何学分科会特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] 対称空間上のベクトル束、等径関数とラドン変換2009

    • Author(s)
      長友康行
    • Organizer
      筑波大学微分幾何学研究集会-伊藤教授退職記念-
    • Place of Presentation
      筑波大学
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体内の全測地的部分多様体2009

    • Author(s)
      長友康行
    • Organizer
      第14回湯沢研究会
    • Place of Presentation
      湯沢グランドホテル
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体内の全測地的部分多様体2009

    • Author(s)
      長友康行
    • Organizer
      日本数学会 幾何学分科会 一般講演
    • Place of Presentation
      大阪大学
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体内の全測地的部分多様体2009

    • Author(s)
      長友康行
    • Organizer
      部分多様体論とその周辺領域における新たな研究対象
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体への調和写像2009

    • Author(s)
      長友康行
    • Organizer
      日本数学会 幾何学分科会 特別講演
    • Place of Presentation
      東京大学
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体への調和写像2009

    • Author(s)
      長友康行
    • Organizer
      名城大学研究集会
    • Place of Presentation
      名城大学
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体への調和写像2008

    • Author(s)
      長友 康行
    • Organizer
      日本数学会幾何学分科会一般講演
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Harmonic maps into Grassmannian manifolds2008

    • Author(s)
      長友康行
    • Organizer
      第16回国際学術シンポジウム「リーマン面、調和写像と可視化」
    • Place of Presentation
      大阪市立大学
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体への調和写像2008

    • Author(s)
      長友康行
    • Organizer
      第13回湯沢研究会
    • Place of Presentation
      湯沢グランドホテル
    • Related Report
      2010 Final Research Report
  • [Presentation] Totally geodesic immersions into Grassmannian manifolds2008

    • Author(s)
      長友康行
    • Organizer
      14th International Symposium on Complex Geometry
    • Place of Presentation
      菅平高原プチホテルゾンタック
    • Related Report
      2010 Final Research Report
  • [Presentation] グラスマン多様体への調和写像2008

    • Author(s)
      長友康行
    • Organizer
      日本数学会 幾何学分科会 一般講演
    • Place of Presentation
      東京工業大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Totally geodesic immersion into Grassmannian manifolds2008

    • Author(s)
      長友康行
    • Organizer
      JSPS-RFBR Workshop Harmonic Analysis on Homogeneous Spaces and Quantization
    • Place of Presentation
      東京大学玉原セミナーハウス
    • Related Report
      2010 Final Research Report

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

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