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A construction of the thery of homogeneous surfaces in Riemannian symmetric spaces

Research Project

Project/Area Number 16K05133
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionYamaguchi University

Principal Investigator

Naitoh Hiroo  山口大学, その他部局等, 名誉教授 (10127772)

Co-Investigator(Kenkyū-buntansha) 井ノ口 順一  筑波大学, 数理物質系, 教授 (40309886)
間下 克哉  法政大学, 理工学部, 教授 (50157187)
中内 伸光  山口大学, 大学院創成科学研究科, 教授 (50180237)
近藤 慶  岡山大学, 自然科学研究科, 教授 (70736123)
Project Period (FY) 2016-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords微分幾何 / 部分多様体 / リーマン対称空間 / グラスマン幾何 / 曲面論 / リー理論 / 準線形偏微分方程式 / 等質部分多様体 / リーマン幾何 / 対称空間
Outline of Final Research Achievements

This research is positioned as the initial research of a research project that considers the classification of homogeneous submanifolds in the Riemannian symmetric spaces from the viewpoint of the Grassmann geometry of submanifolds, and
the target submanifolds are limited to surfaces. The results obtained in this research led to the construction of a general theory regarding the framework of the Grassmann geometry of surfaces, and as a related research, gave the completion of the surface theory of Grassmann geometry in the three-dimensional Riemannian homogeneous space.

Academic Significance and Societal Importance of the Research Achievements

リーマン対称空間の等質部分多様体の分類は未解決問題であり,1950 年代にE.B.Dynkin によって解決されたコンパクトリー群の連結閉部分群の分類問題の発展的課題である。その課題に対する初動的な本研究は、等質曲面をグラスマン幾何的に類別する方法の一般論を考察することで、上記未解決分類問題への1つのアプローチの方法を与えたという点で学術的意義があり、関連研究である3次元リーマン等質空間での研究成果はその方向性が有効であることを示唆している。

Report

(6 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (29 results)

All 2020 2019 2018 2017 2016

All Journal Article (13 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 13 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (16 results) (of which Int'l Joint Research: 3 results,  Invited: 14 results)

  • [Journal Article] Differentiable sphere theorems whose comparison spaces are standard sphere or exotic ones2020

    • Author(s)
      Kei Kondo, Minoru Tanaka
    • Journal Title

      Kodai Mathematical Journal

      Volume: 43 Pages: 349-365

    • NAID

      130007872701

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Grassmann geometry on the 3-dimensional non-unimodular Lie groups2019

    • Author(s)
      Jun-ichi Inoguchi, Hiroo Naitoh
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 48 Pages: 385-406

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Magnetic curves on tangent sphere bundles2019

    • Author(s)
      Jun-ichi Inoguchi, Marian Ioan Munteanu
    • Journal Title

      Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas

      Volume: 113 Issue: 3 Pages: 2087-2112

    • DOI

      10.1007/s13398-018-0600-2

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Non-flat totally geodesic surfaces in symmetric spaces of classical type2019

    • Author(s)
      Katsuya Mashimo
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 56 Pages: 1-32

    • NAID

      120006550803

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Remarks on weakly stationary maps into spheres2018

    • Author(s)
      Masashi Misawa, Nobumitsu Nakauchi
    • Journal Title

      Rend. Circ. Mat. Palermo, II. Ser

      Volume: 印刷中 Issue: 1 Pages: 227-236

    • DOI

      10.1007/s12215-018-0350-1

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Magnetic vector fields: new examples2018

    • Author(s)
      Jun-ichi Inoguchi, Marian Ioan Munteanu
    • Journal Title

      Institut Mathematique. Publications. Nouvelle Serie 117)(Beograd) (N.~S)

      Volume: 103(117) Issue: 117 Pages: 91-102

    • DOI

      10.2298/pim1817091i

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Magnetic curves in tangent sphere bundles II2018

    • Author(s)
      Jun-ichi Inoguchi, Marian Ioan Munteanu
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 466 Issue: 2 Pages: 1570-1581

    • DOI

      10.1016/j.jmaa.2018.06.069

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Grassmann geometry on the 3-dimensional non-unimodular Lie groups(掲載受理)2018

    • Author(s)
      Jun-ichi Inoguchi, Hiroo Naitoh
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: -

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] PERIODIC MAGNETIC CURVES IN BERGER SPHERES2017

    • Author(s)
      Inoguchi Jun-ichi、Munteanu Marian Ioan
    • Journal Title

      Tohoku Mathematical Journal, Second Series

      Volume: 69 Issue: 1 Pages: 113-128

    • DOI

      10.2748/tmj/1493172131

    • ISSN
      0040-8735, 2186-585X
    • Year and Date
      2017-03-30
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Approximations of Lipschitz maps via immersions2017

    • Author(s)
      Kei Kondo, Minoru Tanaka
    • Journal Title

      Nonlinear Analysis

      Volume: 155 Pages: 219-249

    • DOI

      10.1016/j.na.2017.01.022

    • Related Report
      2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Special Lagrangian submanifolds invariant under the isotropy action of symmetric spaces of rank two2016

    • Author(s)
      Kaname Hashimoto and Katsuya Mashimo
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 68 Pages: 839-862

    • NAID

      130006887154

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] A loop group method for affine harmonic maps into Lie groups2016

    • Author(s)
      Josef F. Dorfmeister, Jun-ichi Inoguchi, Shimpei Kobayashi
    • Journal Title

      Advances in Mathematics

      Volume: 298 Pages: 207-253

    • DOI

      10.1016/j.aim.2016.04.018

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Stability of stationary maps of a functional related to pullbacks of metrics2016

    • Author(s)
      Shigeo Kawai and Nobumitsu Nakauchi
    • Journal Title

      Differential Geometry and its Applications

      Volume: 44 Pages: 161-177

    • DOI

      10.1016/j.difgeo.2015.11.005

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Presentation] 3次元等質空間内の曲面のグラスマン幾何2019

    • Author(s)
      井ノ口順一
    • Organizer
      北九州幾何学研究集会2019, 九州工業大学(戸畑キャンパス)
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Slant Curves in contact geometry2019

    • Author(s)
      Inoguchi, Jun-ichi
    • Organizer
      International Workshop on Geometry of Submanifolds 2019, Istanbul center for mathematical Science(トルコ,イスタンブール)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] リーマン幾何における薄滑解析とリプシッツ写像の近似定理2019

    • Author(s)
      近藤 慶
    • Organizer
      合宿セミナー 2019 in 倉敷,倉敷山陽ハイツ(岡山県・倉敷市)
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] リーマン対称空間のグラスマン幾何的曲面論2018

    • Author(s)
      内藤博夫
    • Organizer
      部分多様体幾何とリー群作用2018, 東京理科大学
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] AI型対称空間の不変交代形式について2018

    • Author(s)
      間下克哉
    • Organizer
      広島幾何学研究集会2018
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Harmonic map into Lie groups2018

    • Author(s)
      井ノ口順一
    • Organizer
      The Joint International Meeting of the Chinese mathematical Society and American Mathematical Society
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 写像の共形性に関する変分問題と, その研究過程で現れた変分問題2018

    • Author(s)
      中内伸光
    • Organizer
      金沢研究集会「多様体上の微分方程式」
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 対称空間とグラスマン幾何(連続講演)2018

    • Author(s)
      内藤博夫
    • Organizer
      第17回 秋葉原微分幾何セミナー
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Classification of Cartan embeddings which are austere submanifolds2018

    • Author(s)
      間下克也
    • Organizer
      淡路島幾何学研究集会2018
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Hopfのピンチング予想から微分異種球面定理へ2018

    • Author(s)
      近藤慶
    • Organizer
      日本数学会,2018年度年会春分科会
    • Related Report
      2017 Research-status Report
  • [Presentation] 対称空間とグラスマン幾何2017

    • Author(s)
      内藤博夫
    • Organizer
      小磯憲史先生退職記念研究集会
    • Place of Presentation
      大阪大学(大阪府豊中市)
    • Year and Date
      2017-03-13
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] リー環の外部自己同型とワイル群2017

    • Author(s)
      間下克哉
    • Organizer
      淡路島幾何学研究集会 2017
    • Place of Presentation
      淡路島・国民宿舎 慶野松原荘(兵庫県南あわじ市)
    • Year and Date
      2017-01-27
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Grassmann geometry of surfaces in 3-dimensional homogeneous spaces(基調講演)2017

    • Author(s)
      井ノ口順一
    • Organizer
      International Conference on Applied and Pure Mathematics (ICAPM 2017)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 計量の pullback に関連したある汎関数の stationary map について2017

    • Author(s)
      河合茂生, 中内伸光
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京(東京都八王子市)
    • Related Report
      2016 Research-status Report
  • [Presentation] 平面曲線と意匠設計2016

    • Author(s)
      井ノ口順一
    • Organizer
      第63回幾何学シンポジウム
    • Place of Presentation
      岡山大学(岡山県・岡山市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 薄滑解析と微分球面定理(特別講演)2016

    • Author(s)
      近藤 慶
    • Organizer
      日本数学会 2016年度秋季総合分科会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Related Report
      2016 Research-status Report
    • Invited

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Published: 2016-04-21   Modified: 2022-01-27  

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