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Constructing structure theories of quandles and discrete symmetric spaces

Research Project

Project/Area Number 16K13757
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionOsaka City University (2018)
Hiroshima University (2016-2017)

Principal Investigator

Tamaru Hiroshi  大阪市立大学, 大学院理学研究科, 教授 (50306982)

Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsカンドル / 対称空間 / 幾何学
Outline of Final Research Achievements

We obtained results on disconnected flat quandles and on symmetry-commutative subsets in quandles. In the former, we construct disconnected flat quandles from any graph, and proved that the constructed quandle is homogeneous if and only if the graph is vertex-transitive. In the latter, we defined the notion of symmetry-commutative subsets in quandles, and determined them for many cases, such as oriented Grassmannians and compact classical Lie groups.

Academic Significance and Societal Importance of the Research Achievements

本研究では,対称空間論を参考として,様々な概念や手法をカンドルに対して導入し,その性質を明らかにしている。対称空間論とカンドルを結びつける研究は独自のものであり,新たな研究領域を開拓しているものだと考える。さらにカンドルの研究を通して,対称空間の研究にも新たな知見が付け加えられている。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (31 results)

All 2019 2018 2017 2016 Other

All Journal Article (12 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 11 results,  Acknowledgement Compliant: 3 results) Presentation (18 results) (of which Int'l Joint Research: 10 results,  Invited: 14 results) Remarks (1 results)

  • [Journal Article] Curvature properties of homogeneous real hypersurfaces in nonflat complex space forms2018

    • Author(s)
      Sadahiro Maeda, Hiroshi Tamaru, Hiromasa Tanabe
    • Journal Title

      Kodai Mathematical Journal

      Volume: 41 Issue: 2 Pages: 315-331

    • DOI

      10.2996/kmj/1530496844

    • NAID

      130007402838

    • ISSN
      0386-5991, 1881-5472
    • Year and Date
      2018-06-30
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces2018

    • Author(s)
      Jong Taek Cho, Takahiro Hashinaga, Akira Kubo, Yuichiro Taketomi, Hiroshi Tamaru
    • Journal Title

      J. Geom. Phys.

      Volume: 123 Pages: 221-234

    • DOI

      10.1016/j.geomphys.2017.08.013

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the nonexistence of left-invariant Ricci solitons --- a conjecture and examples2018

    • Author(s)
      Yuichiro Taketomi, Hiroshi Tamaru
    • Journal Title

      Transf. Groups

      Volume: 23 Issue: 1 Pages: 257-270

    • DOI

      10.1007/s00031-017-9439-4

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] 対称空間論の離散化とカンドル代数, Part III2018

    • Author(s)
      Hiroshi Tamaru
    • Journal Title

      第35回代数的組合せ論シンポジウム記録集

      Volume: 35

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Three-dimensional solvsolitons and the minimality of the corresponding submanifolds2017

    • Author(s)
      Takahiro Hashinaga, Hiroshi Tamaru
    • Journal Title

      Internat. J. Math.

      Volume: 28 Issue: 06 Pages: 1750048-1750048

    • DOI

      10.1142/s0129167x17500483

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] The solvable models of noncompact real two-plane Grassmannians and some applications2017

    • Author(s)
      Jong Taek Cho, Takahiro Hashinaga, Akira Kubo, Yuichiro Taketomi, Hiroshi Tamaru
    • Journal Title

      Hermitian-Grassmannian Submanifolds

      Volume: 203 Pages: 311-321

    • DOI

      10.1007/978-981-10-5556-0_26

    • ISBN
      9789811055553, 9789811055560
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] HOMOGENEOUS RICCI SOLITON HYPERSURFACES IN THE COMPLEX HYPERBOLIC SPACES2016

    • Author(s)
      Takahiro Hashinaga, Akira Kubo, Hiroshi Tamaru
    • Journal Title

      Tohoku Mathematical Journal, Second Series

      Volume: 68 Issue: 4 Pages: 559-568

    • DOI

      10.2748/tmj/1486177215

    • NAID

      130008144991

    • ISSN
      0040-8735, 2186-585X
    • Year and Date
      2016-12-30
    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Milnor-type theorems for left-invariant Riemannian metrics on Lie groups2016

    • Author(s)
      Takahiro Hashinaga, Hiroshi Tamaru, Kazuhiro Terada
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 68 Issue: 2 Pages: 669-684

    • DOI

      10.2969/jmsj/06820669

    • NAID

      130006887138

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] On classification of quandles of cyclic type2016

    • Author(s)
      Seiichi Kamada, Hiroshi Tamaru, Koshiro Wada
    • Journal Title

      Tokyo J. Math.

      Volume: 39 Issue: 1 Pages: 157-171

    • DOI

      10.3836/tjm/1459367262

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The space of left-invariant Riemannian metrics2016

    • Author(s)
      Hiroshi Tamaru
    • Journal Title

      Springer Proc. Math. Stat.

      Volume: 154 Pages: 315-326

    • DOI

      10.1007/978-4-431-56021-0_17

    • ISBN
      9784431560197, 9784431560210
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Flat connected finite quandles2016

    • Author(s)
      Yoshitaka Ishihara, Hiroshi Tamaru
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 144 Issue: 11 Pages: 4959-4971

    • DOI

      10.1090/proc/13095

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups2016

    • Author(s)
      Akira Kubo, Kensuke Onda, Yuichiro Taketomi, Hiroshi Tamaru
    • Journal Title

      Hiroshima Math. J.

      Volume: 46 Pages: 357-374

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Presentation] サッカーの幾何学:変分法に基づくゴールキーパーの最適位置2019

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      淡路島幾何学研究集会 2019
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Examples of weakly reflective submanifolds in noncompact symmetric spaces2018

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      Hiroshima Differential Geometry Day 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Flat quandles, graphs, and subsets in symmetric spaces2018

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      第35回代数的組合せ論シンポジウム
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Flat quandles, graphs, and subsets in symmetric spaces2018

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      広島大学数学教室談話会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Symmetric spaces, submanifold geometry, and left-invariant metrics2018

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      OCAMI 談話会
    • Related Report
      2018 Annual Research Report
  • [Presentation] カンドルおよび対称空間内のある種の部分集合2018

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      部分多様体論・湯沢2018
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Left-invariant pseudo-Riemannian metrics on some solvable Lie groups2018

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      AMS Special Session on Nilpotent and Solvable Geometry (San Diego, California)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Flat quandles and finite subsets in symmetric spaces2018

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      Hakata Workshop Winter Meeting 2018: Discrete Mathematics and its Applications
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Left-invariant pseudo-Riemannian metrics on some Lie groups2018

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      Geometry of Submanifolds and Integrable Systems (Osaka City University)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Left-invariant metrics and submanifold geometry2017

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      Lie Group Actions in Riemannian Geometry (Dartmouth College, USA)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Symmetric spaces, submanifold geometry, and solvmanifolds2017

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      Capital Normal University-Hiroshima University Joint Conference on Mathematics
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] カンドルにおける平坦性と可換性2017

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      北九州ワークショップ「幾何学と組合せ論」
    • Place of Presentation
      リファレンス小倉魚町
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Left-invariant metrics and submanifold geometry2017

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      The 7th International Workshop on Differential Geometry
    • Place of Presentation
      虹ノ松原ホテル
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Quandles and discrete symmetric spaces --- flatness and commutativity2017

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      The 13th OCAMI-RIRCM Joint Differential Geometry Workshop on Submanifold Geometry and Lie Theory
    • Place of Presentation
      大阪市立大学
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Ricci soliton and contact homogeneous hypersurfaces in noncompact symmetric spaces2017

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      Workshop on Differential Geometry, Gwangju-2017
    • Place of Presentation
      Chonnam National University, 韓国
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On totally geodesic surfaces in symmetric spaces and applications2016

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      Japan-China Geometry Conference
    • Place of Presentation
      Fujian Normal University, 中国
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 非コンパクト型対称空間への余等質性 1 作用 --- an overview2016

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      合宿セミナー 2016 in 山口
    • Place of Presentation
      山口紅花舎
    • Related Report
      2016 Research-status Report
  • [Presentation] Left-invariant metrics and submanifold geometry2016

    • Author(s)
      Hiroshi Tamaru
    • Organizer
      Differential Geometry, Lie Theory and Low-Dimensional Topology
    • Place of Presentation
      La Trobe University, オーストラリア
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] Tamaru's WEB PAGE

    • URL

      http://www.math.sci.hiroshima-u.ac.jp/~tamaru/index-j.html

    • Related Report
      2016 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2020-03-30  

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