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Research for the twistor theory concerning families of holomorphic disks and geometry of indefinite metrics

Research Project

Project/Area Number 20740034
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionTokyo University of Science (2010-2011)
Tokyo Institute of Technology (2008-2009)

Principal Investigator

NAKATA Fuminori  東京理科大学, 理工学部・数学科, 助教 (80467034)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords微分幾何学 / 複素幾何学 / ツイスター理論 / 波動方程式 / 微分幾何 / 不定値計量 / 正則円板の族
Research Abstract

New general theories, reduction theories and many examples are established in the field of the theory of twistor correspondence concerning with families of holomorphic disks. We obtained new results on the theories of hyperbolic PDEs and integral transforms, and we found unknown relations between twistor theory and these theories. Such relations give new insights to the theory of indefinite geometries. The results in this research give a new way to develop indefinite geometries.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (30 results)

All 2011 2010 2009 2008 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (23 results)

  • [Journal Article] Minitwistor spaces, Severi varieties, and Einstein-Weyl structure2011

    • Author(s)
      Nobuhiro Honda, Fuminori Nakata
    • Journal Title

      Annals of Global Analysis and Geometry

      Volume: 39 Pages: 293-323

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minitwistor spaces, Severi varieties, and Einstein-Weyl structure2011

    • Author(s)
      Nobuhiro Honda, Fuminori Nakata
    • Journal Title

      Annals of Global Analysis and Geometry 39

      Pages: 293-323

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A construction of Einstein-Weyl spaces via LeBrun-Mason type twistor correspondence2009

    • Author(s)
      Fuminori Nakata
    • Journal Title

      Cmmunications in Mathematical Physics

      Volume: 289 Pages: 663-699

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A construction of Einstein-Weyl spaces via LeBrun-Mason type twistor correspondence2009

    • Author(s)
      Fuminori Nakata
    • Journal Title

      Cmmunications in Mathematical Physics 289

      Pages: 663-699

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A construction of Einstein-Weyl spaces via LeBrun-Mason type twistorcorrespondence2009

    • Author(s)
      Fuminori Nakata
    • Journal Title

      Communications in Mathematical Physics (In press)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wave equations and the LeBrun-mason correspondence

    • Author(s)
      Fuminori Nakata
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: (掲載決定)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wave equations and the LeBrun-mason correspondence

    • Author(s)
      Fuminori Nakata
    • Journal Title

      Transactions of the American Mathematical Society (掲載決定)

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Presentation] 3次元不定値Einstein-Weyl構造とそのツイスター対応2011

    • Author(s)
      中田文憲
    • Organizer
      広島幾何学研究集会
    • Place of Presentation
      広島大学
    • Year and Date
      2011-10-07
    • Related Report
      2011 Annual Research Report
  • [Presentation] S^1不変不定値Einstein-Weyl構造とそのツイスター対応2011

    • Author(s)
      中田文憲
    • Organizer
      第58回幾何学シンポジウム
    • Place of Presentation
      山口大学
    • Year and Date
      2011-08-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] 波動方程式とLeBrun-Mason対応について2011

    • Author(s)
      中田文憲
    • Organizer
      第57回幾何学シンポジウム
    • Place of Presentation
      神戸大学
    • Year and Date
      2011-08-08
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Presentation] Einstein-Weyl structure on 3 dimensional Severi varieties.2010

    • Author(s)
      Fuminori Nakata
    • Organizer
      Tambara Workshop on Parabolic Geometries and Related Topics
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2010-11-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] LeBrun-Mason対応と不定値計量の幾何学について2010

    • Author(s)
      中田文憲
    • Organizer
      平成22年日本数学会年会
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-25
    • Related Report
      2011 Final Research Report
  • [Presentation] LeBrun-Mason対応と不定値計量の幾何学について2010

    • Author(s)
      中田文憲
    • Organizer
      平成22年日本数学会年会
    • Place of Presentation
      慶応大学(特別講演)
    • Year and Date
      2010-03-25
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 3次元 Severi 多様体上の Einstein-Weyl 構造2010

    • Author(s)
      中田文憲
    • Organizer
      2010年日本数学会年会
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Wave equations and the LeBrun-Mason twistor correspondence2010

    • Author(s)
      中田文憲
    • Organizer
      第5回日中友好幾何学研究集会
    • Place of Presentation
      沖縄科学技術 研究基盤整備機構
    • Year and Date
      2010-02-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] 波動方程式と Radon 変換および LeBrun-Mason 対応について2009

    • Author(s)
      中田文憲
    • Organizer
      筑波大学微分幾何火曜セミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2009-10-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] 波動方程式と LeBrun-Mason 対応2009

    • Author(s)
      中田文憲
    • Organizer
      大阪市立大学微分幾何学セミナー
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2009-10-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] 「3次元 Severi 多様体上の Einstein-Weyl 構造」,「S^l不変自己双対 Zollfrei 計量と LeBrun-Mason 対応」2009

    • Author(s)
      中田文憲
    • Organizer
      2009年日本数学会秋季総合分科会(一般講演)
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Monopoles and the LeBrun-Mason twistor correspondence2009

    • Author(s)
      中田文憲
    • Organizer
      量子化の幾何学2009
    • Place of Presentation
      早稲田大学
    • Year and Date
      2009-09-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] 3次元Severi多様体上のEinstein-Weyl構造2009

    • Author(s)
      中田文憲
    • Organizer
      第56回幾何学シンポジウム
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-08-31
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] 3次元 Severi 多様体上の Einstein-Weyl 構造2009

    • Author(s)
      中田文憲
    • Organizer
      第56回幾何学シンホジウム(一般講演)
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-08-31
    • Related Report
      2009 Annual Research Report
  • [Presentation] Radon 変換と twistor 理論2009

    • Author(s)
      中田文憲
    • Organizer
      玉原幾何学ミニワークショップ
    • Place of Presentation
      東京大学玉原国際 セミナーハウス
    • Year and Date
      2009-08-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] Wave equation, Funk transform and the LeBrun-Mason twistor theroy2009

    • Author(s)
      中田文憲
    • Organizer
      Workshop on Integral Geometry and Group Representations
    • Place of Presentation
      東京大学玉原国際 セミナーハウス
    • Year and Date
      2009-08-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] Wave equation, Funk transform, and the LeBrun-Mason twistor theory2009

    • Author(s)
      Fuminori Nakata
    • Organizer
      国際研究集会『Workshop on Integral Geometry and Group Representations』
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2009-07-22
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Monopoles and the LeBrun-Mason twistor correspondence2009

    • Author(s)
      中田文憲
    • Organizer
      第13回他変数関数論葉山シンポジウム
    • Place of Presentation
      湘南国際村センター
    • Year and Date
      2009-07-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] LeBrun-Mason対応について2009

    • Author(s)
      中田文憲
    • Organizer
      研究集会『擬リーマン幾何の展開』
    • Place of Presentation
      お茶の水女子大学
    • Year and Date
      2009-02-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] LeBrun-Mason type twistor correspondence for Einstein-Weyl structures2008

    • Author(s)
      中田文憲
    • Organizer
      第55回幾何学シンポジウム
    • Place of Presentation
      弘前大学
    • Year and Date
      2008-08-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] LeBrun-Mason type twistor correspondence for Einstein-Weyl structures2008

    • Author(s)
      Fuminori Nakata
    • Organizer
      国際研究集会『Geometry, Integrability, and Twistor Theory』
    • Place of Presentation
      Cambridge Univ. UK
    • Year and Date
      2008-06-25
    • Related Report
      2011 Final Research Report
  • [Presentation] LeBrun-Mason type twistor correspondence for Einstein-Weyl structures2008

    • Author(s)
      Fuminori Nakata
    • Organizer
      国際研究集会『Geometry, Integrability, and Twistor Theory』
    • Place of Presentation
      Cambridge Univ.UK
    • Year and Date
      2008-06-25
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] LeBrun-Mason type twistor correspondence for Einstein-Weylstructures2008

    • Author(s)
      Fuminori Nakata
    • Organizer
      国際研究集会『Geometry, Integrability, and Twistor Theory』
    • Place of Presentation
      Cambridge Univ. UK
    • Year and Date
      2008-06-25
    • Related Report
      2008 Annual Research Report

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

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