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Applications to differential geometry associated with the recent progress in computer algebra

Research Project

Project/Area Number 18540104
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

HAMADA Tatsuyoshi  Fukuoka University, 理学部, 助教 (90299537)

Research Collaborator 中川 義行  京都産業大学, 非常勤講師
横田 博史  東芝インフォメーションシステムズ, システムエンジニア
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,740,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥540,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywords幾何学 / 応用数学 / 計算機システム / KNOPPIX
Research Abstract

本研究では、計算代数の最新の研究成果を元に微分幾何学への応用と新たな研究手法の展開をはかった. 本研究の成果として, 複素空間型内の正則接分布が可積分な*-アインシュタイン実超曲面を決定した. また, 複素2次元複素空間型内のホップ擬対称実超曲面を決定した. 研究対象を階数1コンパクト対称空間内の実超曲面に拡張し, 測地線の大域的な挙動により, 主曲率が特定の条件を満たす完備実超曲面が測地球に限ることを示した. 計算代数分野との交流により, 最新の計算機代数システムおよび可視化ソフトウェアを収録したDVD起動型LinuxシステムKNOPPIX/Mathの開発, 公開を行った.

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (40 results)

All 2008 2007 2006 Other

All Journal Article (8 results) (of which Peer Reviewed: 7 results) Presentation (17 results) Remarks (15 results)

  • [Journal Article] , KNOPPIX/Math:A live system for enjoying mathematics with computer2008

    • Author(s)
      Tatsuyoshi Hamada and KNOPPIX/Math committers
    • Journal Title

      Abstracts of the Software Exhibi tions Session, ISSA C2008, International Symposium on Symbolic and Algebraic Compu ting RISC Hagenberg Austria July 20-23 2008, ACM Communications in Computer Algebra 42,No.3

      Pages: 175-176

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] KNOPPIX/Math : A live system for enjoying mathematics with computer2008

    • Author(s)
      Tatsuyoshi Hamada, KNOPPIX/Math committers
    • Journal Title

      ACM Communications in Computer Algebra 42

      Pages: 175-176

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] KNOPPIX/Math : Portable and distributable collection of mathematical software and free documents2006

    • Author(s)
      Tatsuyoshi Hamada, Kuniyasu Suzaki, Kengo Iijima, Arimitsu Shikoda
    • Journal Title

      Mathematical Software -ICMS2006, Lecture Notes in Computer Science(Springer) 4151

      Pages: 385-390

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] KNOPPIX/Math : Portable and distributable collection of mathematical software and free documents.2006

    • Author(s)
      Hamada, T., Suzuki, K., Iijima, K., Shikoda, A
    • Journal Title

      Lecture Notes in Computer Science, Springer 4151

      Pages: 285-290

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Complete real hypersurfaces in compact rank one symmetric spaces

    • Author(s)
      Tatsuyoshi Hamada, Katsuhiro Shiohama
    • Journal Title

      Proc. Amer. Math. Soc. (掲載予定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On three dimensional real hypersurfaces in complex space form

    • Author(s)
      Jong-Taek Cho, Tatsuyoshi Hamada, Jun-ichi Inoguchi
    • Journal Title

      Tokyo Journal of Mathematics (掲載予定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On three dimensional real hypersurface in complex space form

    • Author(s)
      Jong-Taek Cho, Tatsuyoshi Hamada, Jun-ichi Inoguchi
    • Journal Title

      Tokyo Journal of Mathematics (掲載確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complete real hypersurfaces in compact rank one symmetric spaces

    • Author(s)
      Tatsuyoshi Hamada, Katsuhiro Shiohama
    • Journal Title

      Proceedings of American Mathematical Society (掲載確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 数学ソフトウェア最新事情2008

    • Author(s)
      濱田龍義
    • Organizer
      ワークショップ「数学ソフトウェアとフリードキュメントVII」
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-23
    • Related Report
      2008 Final Research Report
  • [Presentation] 複素空間型内の実超曲面に関する考察2008

    • Author(s)
      濱田龍義
    • 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 Final Research Report
  • [Presentation] KNOPPIX/Math: A Live system for enjoying mathematics with computer2008

    • Author(s)
      Tatsuyoshi Hamada, and KNOPPIX/Math committers
    • Organizer
      ISSAC2008
    • Place of Presentation
      RISC-LINZ, Hagenberg, Austria
    • Year and Date
      2008-07-21
    • Related Report
      2008 Final Research Report
  • [Presentation] KNOPPIX/Math/2008について2008

    • Author(s)
      濱田龍義
    • Organizer
      日本数式処理学会
    • Place of Presentation
      城西大学東京紀尾井町キャンパス
    • Year and Date
      2008-06-06
    • Related Report
      2008 Final Research Report
  • [Presentation] KNOPPIX/Math/2008について2008

    • Author(s)
      演田龍義
    • Organizer
      数式処理学会
    • Place of Presentation
      城西大学紀尾井町キャンパス
    • Year and Date
      2008-06-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] KNOPPIX/Math: computer environment for mathematics2008

    • Author(s)
      Tatsuyoshi Hamada
    • Organizer
      The twelfth international workshop on differential geometry and related topics
    • Place of Presentation
      Kyungpook National University, Taegu, Korea
    • Year and Date
      2008-05-31
    • Related Report
      2008 Final Research Report
  • [Presentation] *-Einstein real hypersurfaces of complex space forms2008

    • Author(s)
      Tatsuyoshi Hamada
    • Organizer
      The twelfth international workshop on differential geometry and relatedtopics
    • Place of Presentation
      Kyungpook National University, Taegu, Korea
    • Year and Date
      2008-05-31
    • Related Report
      2008 Final Research Report
  • [Presentation] 数学ソフトウェアの森KNOPPIX/Math2007

    • Author(s)
      濱田龍義
    • Organizer
      第7回「代数学と計算」研究集会(AC2007)
    • Place of Presentation
      首都大学東京
    • Year and Date
      2007-12-06
    • Related Report
      2008 Final Research Report
  • [Presentation] 複素双曲空間内の実超曲面について2007

    • Author(s)
      濱田龍義
    • Organizer
      第54回幾何学シンポジウム
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2007-08-25
    • Related Report
      2008 Final Research Report
  • [Presentation] KNOPPIX/Math作成方法2007

    • Author(s)
      濱田龍義
    • Organizer
      数式処理の新たな発展
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-07-05
    • Related Report
      2008 Final Research Report
  • [Presentation] DVD起動による数学ソフトウェア環境について2007

    • Author(s)
      濱田龍義
    • Organizer
      日本数式処理学会
    • Place of Presentation
      加計学園国際学術交流センター
    • Year and Date
      2007-06-05
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] KNOPPIX/Math2006

    • Author(s)
      Tatsuyoshi Hamada
    • Organizer
      Software for Algebraic Geometry
    • Place of Presentation
      IMA, Minnesota University, USA
    • Year and Date
      2006-10-23
    • Related Report
      2008 Final Research Report
  • [Presentation] KNOPPIX/Math : Portable and distributable collection of mathematical software and free documents2006

    • Author(s)
      Tatsuyoshi Hamada, Kuniyasu Suzaki, Kengo Iijima and Arimitsu Shikoda
    • Organizer
      ICMS2006
    • Place of Presentation
      Castro Urdiales, La Residencia, Spain
    • Year and Date
      2006-09-02
    • Related Report
      2008 Final Research Report
  • [Presentation] 対話式幾何学ソフトウェアについて2006

    • Author(s)
      濱田龍義
    • Organizer
      第53回幾何学シンポジウム
    • Place of Presentation
      金沢大学
    • Year and Date
      2006-08-07
    • Related Report
      2008 Final Research Report
  • [Presentation] 最新KNOPPIX/Math入門2006

    • Author(s)
      濱田龍義
    • Organizer
      日本応用数理学会「教諭アルゴリズムとその応用(JANT)」第15回研究集会,
    • Place of Presentation
      首都大学東京
    • Year and Date
      2006-07-06
    • Related Report
      2008 Final Research Report
  • [Presentation] 対話式幾何学ソフトウェアの応用について2006

    • Author(s)
      濱田龍義
    • Organizer
      日本数式処理学会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2006-06-06
    • Related Report
      2008 Final Research Report
  • [Presentation] KNOPPIX/Math Projectについて2006

    • Author(s)
      濱田龍義
    • Organizer
      第1回IPAB(NPO並列生物情報処理イニシアティブ)セミナー「Knoppix技術の最新動向2006」
    • Place of Presentation
      山王パークタワー
    • Year and Date
      2006-05-26
    • Related Report
      2008 Final Research Report
  • [Remarks] 報道関連情報(計1件)

    • Related Report
      2008 Final Research Report
  • [Remarks] (1) 2008年12月13日、福岡大学文系センター棟に於いて開催されたオープンソースカンファレンス2008Fukuokaの記事が2008年12月22日,電波新聞に掲載された

    • Related Report
      2008 Final Research Report
  • [Remarks] アウトリーチ(計4件)

    • Related Report
      2008 Final Research Report
  • [Remarks] (1)濱田龍義, 「KNOPPIX/Mathは数学のおもちゃ箱」,オープンソースカンファレンス2009大分2009年3月13日, ソフトパーク第2ソフィアブラザビル2階

    • Related Report
      2008 Final Research Report
  • [Remarks] (2)濱田龍義, 「KNOPPIX/Mathは数学のおもちゃ箱」, オープンソースカンファレンス2008福岡2008年12月13日, 福岡大学

    • Related Report
      2008 Final Research Report
  • [Remarks] (3)濱田龍義, 「数学のおもちゃ箱KNOPPIX/Math」, 日本数学会市民講演会2007年9月24日, エル・パーク仙台セミナーホール

    • Related Report
      2008 Final Research Report
  • [Remarks] (4)濱田龍義, 「KNOPPIX/Math~OSSの可能性~」2007年3月20日, 第2回福岡OSS研究会, 福岡SRPセンタービル2階視聴覚研究室

    • Related Report
      2008 Final Research Report
  • [Remarks] ソフトウェア(計4件)

    • Related Report
      2008 Final Research Report
  • [Remarks] (1) KNOPPIX/Math/2009, 2009年3月24日公開

    • Related Report
      2008 Final Research Report
  • [Remarks] (2) KNOPPIX/Math/2008, 2008年3月8日公開

    • Related Report
      2008 Final Research Report
  • [Remarks] (3) KNOPPIX/Math/2007, 2007年3月12日公開

    • Related Report
      2008 Final Research Report
  • [Remarks] (4)KNOPPIX/Math/ICMS2006, 2006年8月22日公開

    • Related Report
      2008 Final Research Report
  • [Remarks] ホームページ等(計1件)

    • URL

      http://www.knoppix-math.org/

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.knoppix-math.org/

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.knoppix-math.org/

    • Related Report
      2007 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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