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2023 Fiscal Year Annual Research Report

Developments and Applications of Geometric Singularity Theory

Research Project

Project/Area Number 19K03458
Research InstitutionHokkaido University

Principal Investigator

石川 剛郎  北海道大学, 理学研究院, 名誉教授 (50176161)

Project Period (FY) 2019-04-01 – 2024-03-31
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
Outline of Annual Research Achievements

幾何学的特異点論に関する研究として,最終年度において,接可展面の平行曲面の特異点を分類することに成功した(Singularities of parallels to tangent developable surfaces,Tohoku Mathematical Journal, vol.75-2, (2023), 233-249.)また (3,5)型および (4,7)型接分布の特異曲線について研究し出版予定である.また研究期間全体を通じて,国際共同研究を行いシンプレクティック特異点の概説論文 G. Ishikawa and S. Janeczko, Symplectic singularities of differentiable mappings, in Differential geometry, Calabi-Yau theory, and general relativity, Lectures and articles celebrating the 70th birthday of Shing Tung Yau,Surveys in Differential Geometry, Volume 24-II, published in 2021. International Press, pp. 117-172,および特異写像の零形式に関する論文 G. Ishikawa, S. Janeczko, Singular mappings and their zero-forms, Pure and Applied Mathematics Quarterly, Volume 16, Number 5, (2020) 1643-1657 を発表した. さらに,フロンタルの法写像と接写像の特異点を調べ,また,アフィン直線族の補空間のトポロジー,さらにフロンタル特異点に関する総合報告を執筆し,併せてコフロンタル写像に関する論文,さらにカルタん分布,すなわち(2,3,5)分布の双対性に関する論文 G. Ishikawa, Y. Kitagawa, A. Tsuchida, W. Yukuno, Duality of (2,3,5)-distributions and Lagrangian cone structures, Nagoya Mathematical Journal. Cambridge University Press: 23 January 2020, pp. 1-13.を発表し,また,ナッシュ関数の複雑性に関する結果も得た.

  • Research Products

    (6 results)

All 2024 2023 Other

All Int'l Joint Research (1 results) Journal Article (1 results) (of which Peer Reviewed: 1 results,  Open Access: 1 results) Presentation (4 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results)

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

    • Country Name
      POLAND
    • Counterpart Institution
      ワルシャワ工科大学
  • [Journal Article] Singularities of parallels to tangent developable surfaces2023

    • Author(s)
      Ishikawa Goo
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 75 Pages: 233-249

    • DOI

      10.2748/tmj.20211220

    • 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
    • Invited
  • [Presentation] Singular curves of (3,5)-distributions2023

    • Author(s)
      Goo Ishikawa
    • Organizer
      Extension of the Singularity theory
    • 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
  • [Presentation] Singularity theory of mappings over dual numbers2023

    • Author(s)
      Goo Ishikawa
    • Organizer
      ingularity theory of Differentiable mappings and its applications,
    • Int'l Joint Research / Invited

URL: 

Published: 2024-12-25  

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