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Locally homogeneous Kaehler manifolds and Transformation groups

Research Project

Project/Area Number 18K03284
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Kamishima Yoshinobu  城西大学, 理学部, 特任教授 (10125304)

Co-Investigator(Kenkyū-buntansha) 長谷川 敬三  新潟大学, 人文社会科学系, フェロー (00208480)
Project Period (FY) 2018-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords幾何構造 / 群の対称性 / 非球形多様体 / 幾何的剛性 / 可微分剛性 / Infra-可解タワー / リー群と等質空間 / 等長群 / Aspherical manifold / Divisible manifold / Infra-solv tower / Solvable radical / Large symmetry / Proper action / Infrasolv manifolds / Smooth toral actions / 可縮空間 / 固有作用 / リー群 / 群コホモロジー / 可解ファイバー / Seifert 多様体 / Iterated infrasolv tower / 等長変換群 / 四元数変換群 / 幾何多様体 / 擬エルミート多様体 / 四元数コンタクト多様体 / 三つのReeb場 / 四元数Heisenberg Lie 群 / 可微分qc-変換群Aut(X) / 正則変換群 / CR多様体 / 佐々木多様体 / ケーラー多様体 / Heisenberg Lie 群 / 半単純リー群 / ケーラー構造 / 佐々木構造 / ,Seifert fibering, / Heisenberg リー群 / 局所等質空間 / Homogeneous space / Divisible discrete group / Sasaki manifold / Kaehler Manifold / Group extension / fiber bundle / Solvmaniofd / 等質リーマン空間 / 変換群 / 剛性
Outline of Final Research Achievements

The following were the subjects of my research. I.Structure of Isometry groups with radical,and aspherical Riemannian manifolds with large symmetry. Classification of infra-solv tower of fiber bundles.
(Isometry groups with radical,and aspherical Riemannian manifolds with large symmetry.II.Isometric classification of compact locally homogeneous aspherical
Kaehler, Sasaki manifolds. We proved every compact aspherical Riemannian manifold admits a canonical series of orbibundle structures with infra-solv fibers which is called an infra-solv tower. Its length and the geometry of its base measure the degree of continuous symmetry of an aspherical Riemannian manifold. We show that the manifold has large local symmetry if it admits a tower of orbibundle fibrations with locally homogeneous fibers infra-solv tower whose base is a locally homogeneous space. We constructed examples of aspherical manifolds with large local symmetry, which do not support any locally homogeneous Riemannian metrics.

Academic Significance and Societal Importance of the Research Achievements

研究成果の社会への発信は東京という地理的条件もあり大学をあげて努めた.具体的には城西大学紀尾井町キャンパスにおいてコロキュウムを開催,また坂戸(埼玉)キャンパスではオープンユニバーシティでわかりやすく研究成果の一端を社会に還元している.一方で海外には研究集会(サマースクール(Hamburg)を含む)に赴き長期のスパンでの講義・連続講演を提供することで,社会における基盤としての数学の重要性を世界に伝えている.この分野における学術的な意義として,様々な分野への結果に対する,理論的担保と永久の信頼性を与える数学的基盤の構築を行った.

Report

(7 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
  • 2018 Research-status Report
  • Research Products

    (13 results)

All 2024 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (1 results) Journal Article (8 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 8 results,  Open Access: 6 results) Presentation (4 results) (of which Int'l Joint Research: 3 results,  Invited: 4 results)

  • [Int'l Joint Research] Oliver Baues/University of Fribourg(スイス)

    • Related Report
      2019 Research-status Report
  • [Journal Article] Isometry groups with radical, and aspherical Riemannian manifolds with large symmetry I.2023

    • Author(s)
      O. Baues,Y. Kamishima
    • Journal Title

      Geometry & Topology

      Volume: 27 Issue: 1 Pages: 1-50

    • DOI

      10.2140/gt.2023.27.1

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isometry groups with radical, and aspherical Riemannian manifolds with large symmetry, I2023

    • Author(s)
      O. Baues, Y. Kamishima
    • Journal Title

      Geometry and Topology (近刊)

      Volume: -

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isometry groups with radical, and aspherical Riemannian manifolds with large symmetry I2022

    • Author(s)
      O. Baues, Y. Kamishima
    • Journal Title

      G&T

      Volume: 0 Pages: 0-0

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Quaternionic contact $4n+3$-manifolds and their $4n$-quotients2021

    • Author(s)
      Y. Kamishima
    • Journal Title

      Annals of Global Analysis and Geometry (2021)

      Volume: 59 Issue: 4 Pages: 435-455

    • DOI

      10.1007/s10455-021-09758-5

    • Related Report
      2021 Research-status Report 2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups2021

    • Author(s)
      D. Alekssevsky, K. Hasegawa, Y. Kamishima
    • Journal Title

      Nagoya Math. J.

      Volume: 243 Pages: 83-96

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Construction of contractible complete quaternionic almost Hermitian manifolds with compact isometry group2021

    • Author(s)
      Y. Kamishima
    • Journal Title

      Josai Mathematical Monograph

      Volume: 13 Pages: 52-66

    • NAID

      120007027895

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Locally homogeneous aspherical Sasaki manifolds.2020

    • Author(s)
      O. Baues and Y. Kamishima
    • Journal Title

      Differential Geom. Appl.

      Volume: 70 Pages: 1-41

    • Related Report
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On quaternioic 3 CR-structure and pseudo-Riemannian metric2018

    • Author(s)
      Y. Kamishima
    • Journal Title

      Applied Mathematics (Special Issue on Riemannian Geometry).

      Volume: 9 (2) Pages: 114-129

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Geometric structures on contact Heisenberg nilpotent Lie group.2024

    • Author(s)
      Yoshinobu Kamishima
    • Organizer
      KAIST Geometric Structures Lecture Series.
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] On the fundamental groups of compact aspherical manifolds with parabolic structures.2023

    • Author(s)
      Yoshinobu Kamishima
    • Organizer
      国際研究集会, The Fourth Taiwan-Japan Joint Conference on Differential Geometry
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Locally homogeneous aspherical Sasaki manifolds2019

    • Author(s)
      Y. Kamishima
    • Organizer
      2019 Taipei Conference on Geometric Invariance and Partial Differential Equations
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A Note on Vanishing of Equivariant Cohomology of Proper Actions and Application to the Conformal and CR-automorphism Groups2019

    • Author(s)
      Y. Kamishima
    • Organizer
      The 2nd Taiwan-Japan Joint Conference on Differential Geometry
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2018-04-23   Modified: 2025-01-30  

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