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Research of surfaces in four-dimensional Riemannian manifolds using their twistor lifts

Research Project

Project/Area Number 20740046
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKanazawa University (2009-2011)
Tokyo University of Science (2008)

Principal Investigator

HASEGAWA Kazuyuki  Kanazawa University, 学校教育系, 准教授 (50349825)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsツイスター空間 / ツイスターリフト / 調和切断
Research Abstract

We classify surfaces of genus zero in self-dual Einstein manifolds whose twistor lifts are harmonic sections. Using this result, we obtain a classification for the quotient space of the space of all twistor holomorphis surfaces by conformal transformations in the special case. Moreover we show that twsitor lifts of twistor holomorphic surfaces are weakly stable as harmonic sections if ambient spaces are self-dual Einstein manifolds of non-negative scalar curvature. Conversely, if the ambient space is Euclidean space, a surface whose twistor lift is a weakly stable harmonic section is twistor holomorphic.

Report

(5 results)
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (21 results)

All 2011 2010 2009 2008 Other

All Journal Article (10 results) (of which Peer Reviewed: 9 results) Presentation (10 results) Remarks (1 results)

  • [Journal Article] Surfaces in four-dimensiona hyperkaehler manifolds whose twistor lifts are harmonic sections2011

    • Author(s)
      K Hasegawa
    • Journal Title

      Proc. Amer. Math. Soc

      Volume: 139 Pages: 309-317

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hasegawa, Surfaces in four-dimensiona hyperkaehler manifolds whose twistor lifts are harmonic sections2011

    • Author(s)
      E K.
    • Journal Title

      Proc.Amer.Math.Soc. 139

      Pages: 309-317

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Surfaces in four-dimensional hyperkaehler manifolds whose twistor lifts are harmonic sections2011

    • Author(s)
      K.Hasegawa
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 139 Pages: 309-317

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Surfaces in hyperkaehler manifolds whose twistor lifts are harmonic sections2010

    • Author(s)
      長谷川和志
    • Journal Title

      研究集会「部分多様体幾何とリー群作用」報告集

    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Journal Article] On surfaces of low genus whose twistor lifts are harmonic sections2010

    • Author(s)
      K. Hasegawa
    • Journal Title

      Journal of Geometry and Symmetry in Physics

      Volume: 17 Pages: 35-43

    • Related Report
      2010 Annual Research Report 2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On surfaces of low genus whose twistor lifts are harmonic sections2010

    • Author(s)
      K.Hasegawa
    • Journal Title

      Journal of Geometry and Symmetry in Physics 17

      Pages: 35-43

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Stability of twistorlifts for surfaces in four-dimensional manifolds as harmonic sections2009

    • Author(s)
      K. Hasegawa
    • Journal Title

      J. Geom. Phys

      Volume: 59 Pages: 1326-1338

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability of twistor lifts for surfaces in four-dimensional manifolds as harmonic sections2009

    • Author(s)
      K.Hasegawa
    • Journal Title

      J.Geom.Phys. 59

      Pages: 1326-1338

    • Related Report
      2010 Self-evaluation Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A generalization of Cartan's identities for isoparametric hypersurfaces and its applications2008

    • Author(s)
      N Abe and K Hasegawa
    • Journal Title

      Result. Math

      Volume: 52 Pages: 197-210

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A generalization of Cartan's identities for isoparametric hypersurfaces and its applications2008

    • Author(s)
      N. Abe and K. Hasegawa
    • Journal Title

      Result. Math 52

      Pages: 197-210

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Surfaces of genus zero in self-dual Einstein manifolds and their twistor lifts2010

    • Author(s)
      K. Hasegawa
    • Organizer
      International Conference "Differential Geometry andits Applications"
    • Place of Presentation
      ブルノ(チェコ)
    • Year and Date
      2010-08-28
    • Related Report
      2010 Final Research Report
  • [Presentation] Surfaces of genus zero in self-dual Einstein manifolds and their twistor lifts2010

    • Author(s)
      K.Hasegawa
    • Organizer
      International Conference Differential Geometry and its Applications
    • Place of Presentation
      マサリスク大学(チェコ・ブルノ)
    • Year and Date
      2010-08-28
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Surfaces of genus zero in self-dual Einstein manifolds and their twistor lifts2010

    • Author(s)
      K.Hasegawa
    • Organizer
      International Conference"Differential Geometry and its Applications"
    • Place of Presentation
      マサリスク大学(ブルノ・チェコ)
    • Year and Date
      2010-08-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Surfaces in hyperkaehler manifolds whose twistor lifts are harmonic sections2009

    • Author(s)
      長谷川和志
    • Organizer
      研究集会「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(東京都)
    • Year and Date
      2009-09-08
    • Related Report
      2010 Self-evaluation Report 2010 Final Research Report
  • [Presentation] Surfaces in hyperkaehler manifolds whose twistor lifts are harmonic sections2009

    • Author(s)
      長谷川和志
    • Organizer
      研究集会"部分多様体幾何とリー群作用"
    • Place of Presentation
      東京理科大学(東京都)
    • Year and Date
      2009-09-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Surfaces in four-dimensional Euclidean space whose twistor lifts are harmonic sections2009

    • Author(s)
      長谷川和志
    • Organizer
      日本数学会秋季総合分科会幾何学分科会
    • Place of Presentation
      大阪大学(大阪府)
    • Year and Date
      2009-09-02
    • Related Report
      2010 Self-evaluation Report 2010 Final Research Report 2009 Annual Research Report
  • [Presentation] On low genus surfaces whose twistor lifts are harmonic sections2009

    • Author(s)
      K. Hasegawa
    • Organizer
      The 11th International Conference "Geometry, Integrability and Quantization"
    • Place of Presentation
      バルナ(ブルガリア)
    • Year and Date
      2009-06-05
    • Related Report
      2010 Final Research Report
  • [Presentation] On low genus surfaces whose twistor lifts are harmonic sections The llth International Conference Geometry2009

    • Author(s)
      K.Hasegawa
    • Organizer
      Integrability and Quantization
    • Place of Presentation
      パノラマホテル(ブルガリア・バルナ)
    • Year and Date
      2009-06-05
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On low genus surfaces whose twistor lifts are harmonic sections2009

    • Author(s)
      K.Hasegawa
    • Organizer
      The 11th International Conference "Geometry, Integrability and Quantization"
    • Place of Presentation
      (ブルガリア)・ヴァルナ
    • Year and Date
      2009-06-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] On low genus surfaces whose twistor lifts are harmonic sections2009

    • Author(s)
      長谷川和志
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.ed.kanazawa-u.ac.jp/~kazuhase/

    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2017-05-19  

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