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Developments and Applications of Geometric Singularity Theory

Research Project

Project/Area Number 19K03458
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11020:Geometry-related
Research InstitutionHokkaido University

Principal Investigator

Ishikawa Goo  北海道大学, 理学研究院, 名誉教授 (50176161)

Project Period (FY) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsフロンタル / 幾何学的制御理論 / サブリーマン幾何 / 特異曲線 / 接触構造 / 単純リー環 / 接分布 / 双対性 / frontal / singular curve / C3 distribution / double number / frontal jet / parallel / Frontal / Tangent map / Parallel / normally flat / singular surface / abnormal geodesics / Parallel frontals / Tangent mapping / Zero-form / Normally parallel / Tangentially parallel / Normal mapping / Parametric singularities / Singular curve / シンプレクティック構造 / ラグランジュ多様体 / ルジャンドル多様体 / コフロンタル / 特異点の認識問題 / 微分式系 / 制御系 / 幾何ロバスト性 / 幾何学化
Outline of Research at the Start

初年度は,九州,京都,静岡などにおける研究会参加し参加者および研究協力者と研究連絡を行う.また,モスクワとワルシャワとバレンシアと海南島などにおける海外の研究会に参加し参加者および研究協力者と研究連絡を行う.本研究と関連する研究を行っている若手研究者を招聘する.次年度以降も含めた研究連絡と成果発表に使用するためにパソコン1台を購入し,研究課題の解決を促進させる.こうして,具体的な研究目標を解決していく.
次年度以降も研究課題の解決のために不可欠な国内出張と海外出張を行い,また必要な物品を購入し,具体的な研究目標を解決するとともに,解決して得られた成果を,順次,発表・公開・出版していく.

Outline of Final Research Achievements

As developments and applications of geometric singularities and, we have succeeded to classify singularities of parallels to developable surfaces. We have investigated singular curves of (3,5) and (4,7) distributions, the results of which are going to be published. During all periods of the research, we have performed international researches, further we have published the survey article on symplectic singularities and studied normal and tangential maps to frontals. Also we published papers on the topology of complements to affine line arrangements, on the duality of Cartan distributions, i.e. (2, 3, 5)-distributions and published results on the complexity of Nash functions. Moreover we have wrote an integrated survey paper on frontal singularities.

Academic Significance and Societal Importance of the Research Achievements

幾何学的特異点論は,数学の中で最も歴史のある幾何学の中で,他分野との関連や応用上重要な視点となる特異点に注目することにより新しい視点を与え,学術的に幾何学の新しい側面に光を照らす研究であり学術的な意義は深く広い.また,空間識,あるいは,時空識の研究への応用が期待されていて,社会的意味も大きいと期待される.

Report

(6 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (36 results)

All 2024 2023 2022 2021 2020 2019 Other

All Int'l Joint Research (5 results) Journal Article (11 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 11 results,  Open Access: 4 results) Presentation (17 results) (of which Int'l Joint Research: 11 results,  Invited: 10 results) Book (1 results) Remarks (2 results)

  • [Int'l Joint Research] ワルシャワ工科大学(ポーランド)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] ワルシャワ工科大学(ポーランド)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Warsaw University of Technology(ポーランド)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] ワルシャワ工科大学(ポーランド)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] モスクワ大学(ロシア連邦)

    • Related Report
      2019 Research-status Report
  • [Journal Article] Singularities of parallels to tangent developable surfaces2023

    • Author(s)
      Ishikawa Goo
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 75 Issue: 2 Pages: 233-249

    • DOI

      10.2748/tmj.20211220

    • Related Report
      2023 Annual Research Report 2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Singularities of parallels to tangent developable surfaces2022

    • Author(s)
      Ishikawa Goo
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 出版確定

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Symplectic singularities of differentiable mappings2021

    • Author(s)
      G. Ishikawa and S. Janeczko
    • Journal Title

      Surveys in Differential Geometry

      Volume: 24 Issue: 1 Pages: 117-172

    • DOI

      10.4310/sdg.2019.v24.n1.a4

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Normal and tangent maps to frontals2021

    • Author(s)
      G. Ishikawa
    • Journal Title

      Journal of Mathematical Sciences

      Volume: 255 Issue: 5 Pages: 664-677

    • DOI

      10.1007/s10958-021-05403-5

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Topology of complements to real affine space line arrangements2020

    • Author(s)
      Ishikawa Goo、Oyama Motoki
    • Journal Title

      Journal of Singularities

      Volume: 22 Pages: 373-384

    • DOI

      10.5427/jsing.2020.22v

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Singular mappings and their zero-forms2020

    • Author(s)
      Goo Ishikawa, Stanislaw Janeczko
    • Journal Title

      Pure and Applied Mathematics Quarterly

      Volume: 16-5 Pages: 1643-1657

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Recognition Problem of Frontal Singularities2020

    • Author(s)
      Ishikawa Goo
    • Journal Title

      Journal of Singularities

      Volume: 21 Pages: 149-166

    • DOI

      10.5427/jsing.2020.21i

    • Related Report
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Singular mappings and their zero-forms.2020

    • Author(s)
      G Ishikawa, S. Janeczko
    • Journal Title

      Pure and Applied Mathematics Quarterly

      Volume: 出版確定

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Duality of (2,3,5)-distributions and Lagrangian cone structures2020

    • Author(s)
      Goo Ishikawa, Yumiko Kitagawa, Asahi Tsuchida, Wataru Yukuno
    • Journal Title

      Nagoya Mathematical Journal

      Volume: 出版確定

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Leibniz complexity of Nash functions on differentiations2019

    • Author(s)
      Goo Ishikawa, Tatsuya Yamashita
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 71-3

    • NAID

      130007682982

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Cofrontals2019

    • Author(s)
      Goo Ishikawa
    • Journal Title

      Romanian Journal of Pure and Applied Mathematics

      Volume: 60-4

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Legendre singularities of sub-Riemannian geodesics and related topics2024

    • Author(s)
      Goo Ishikawa
    • Organizer
      接触構造,特異点,微分方程式及びその周辺
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] Singular curves of (3,5)-distributions2023

    • Author(s)
      Goo Ishikawa
    • Organizer
      Extension of the Singularity theory
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Singularity theory over dual numbers2023

    • Author(s)
      Goo Ishikawa
    • Organizer
      28st (Numadu)-Shizuoka Workshop -- Geometry, Mathematical Physics and Quantum Theory
    • Related Report
      2023 Annual Research Report
  • [Presentation] Singularity theory of mappings over dual numbers2023

    • Author(s)
      Goo Ishikawa
    • Organizer
      ingularity theory of Differentiable mappings and its applications,
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Singularity theory over dual numbers2023

    • Author(s)
      Goo Ishikawa
    • Organizer
      Singularities of Differentiable Maps and its Applications
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] (4, 7) distributions and algebraic curves on tori2023

    • Author(s)
      Goo Ishikawa
    • Organizer
      Singularities of Differentiable Maps and its Applications
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Frontal Jets2023

    • Author(s)
      Goo Ishikawa
    • Organizer
      Singularities of Differentiable Maps and its Applications
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Legendre singularities of sub-Riemannian geodesics2022

    • Author(s)
      Goo Ishikawa
    • Organizer
      Singularity theory and its applications, RIMS-Sing 1 Workshop
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Singular curves of (4, 7) distributions and C_3,2022

    • Author(s)
      Goo Ishikawa
    • Organizer
      Correspondences of various geometries
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Singularities of parallels to tangent developable surfaces2021

    • Author(s)
      Ishikawa Goo
    • Organizer
      24-th Petrovskii Conference, Differential Equations and Related Topics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Singularities of parallels to tangent developable surfaces2021

    • Author(s)
      Ishikawa Goo
    • Organizer
      The Future of Singularity Theory
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] Singularities of parallels to tangent developable surfaces2021

    • Author(s)
      Ishikawa Goo
    • Organizer
      The Sao Carlos Singularity Theory Webinar, UFSCar and ICMC - USP
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Singularities of parallels to tangent maps of frontals,2020

    • Author(s)
      Goo Ishikawa
    • Organizer
      16th International Workshop on Real and Complex Singularities
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Tangential and Normal Maps to Frontals2020

    • Author(s)
      Goo Ishikawa,
    • Organizer
      The International Conference on Differential Equations and Dynamical Systems 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] On Normal and Tangential Maps to Frontals2019

    • Author(s)
      Goo Ishikawa
    • Organizer
      6th International Workshop on Singularities in Generic Geometry and its Applications
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Several problems on singularities of implicit differential equations and related topics2019

    • Author(s)
      Goo Ishikawa
    • Organizer
      Singularity Theory and its Applications in Differential Equations and Differential Geometry
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A remark on the geometric theory of third order ordinary differential equations2019

    • Author(s)
      Goo Ishikawa
    • Organizer
      Muroran Workshop 20
    • Related Report
      2019 Research-status Report
    • Invited
  • [Book] 微積のあたま2022

    • Author(s)
      石川 剛郎
    • Total Pages
      208
    • Publisher
      共立出版
    • ISBN
      9784320114746
    • Related Report
      2022 Research-status Report
  • [Remarks] List of Published Papers by Goo Ishikawa

    • URL

      https://www.math.sci.hokudai.ac.jp/~ishikawa/paper.html

    • Related Report
      2021 Research-status Report
  • [Remarks] List of Published Papers by Goo Ishikawa

    • URL

      http://www.math.sci.hokudai.ac.jp/~ishikawa/paper.html

    • Related Report
      2020 Research-status Report

URL: 

Published: 2019-04-18   Modified: 2025-01-30  

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