左不変な幾何構造の部分多様体論的研究

• Project/Area Number: 26287012
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hiroshima University
• Principal Investigator: 田丸 博士 広島大学, 理学研究科, 教授 (50306982)
• Co-Investigator(Kenkyū-buntansha): 澁谷 一博 広島大学, 理学研究科, 准教授 (00569832) ; 奥田 隆幸 広島大学, 理学研究科, 講師 (40725131) ; 阿賀岡 芳夫 広島大学, 理学研究科, 教授 (50192894)
• Project Period (FY): 2014-04-01 – 2019-03-31
• Project Status: Granted (Fiscal Year 2018)
• Budget Amount: ¥11,180,000 (Direct Cost: ¥8,600,000、Indirect Cost: ¥2,580,000); Fiscal Year 2018: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2017: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2016: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2015: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 幾何学 / 左不変計量 / 対称空間 / 部分多様体 / 左不変幾何構造 / 微分幾何 / リー群

Outline of Annual Research Achievements

(1) カンドルの研究から触発されて，コンパクト対称空間内の「対称可換」な部分集合の研究を行った。今年度は，その一般的な性質を明らかにし，特に具体例として古典型リー群の場合を調べ，その中の対称可換部分集合をほぼ決定することができた。この結果は，論文としてまとめる予定である。
(2) 今年度は10月に「広島幾何学研究集会 2017」を，また12月に「合宿セミナー 2017 in 大久野島」を開催した。それらの機会に，研究分担者および若手の研究協力者達による研究発表もあり，多くの参加者と今後の研究に関する打ち合わせをすることができた。なお本研究費からは，講演者および参加者の旅費や運営に必要な経費等の援助を行った。
(3) 6月に，Dartmouth College (米国) で開催された国際研究集会において招待講演を行った。この研究集会には左不変計量や部分多様体に関する著名な研究者が数多く参加していた。そのような場で，我々の研究成果を発表すると同時に，今後の研究に関する有益な議論をおこなうことができたことは，今後の研究の進展に極めて有益であった。
(4) 9月には，Universitat de Santiago de Compostela (スペイン) に滞在し，現地の若い研究者を対象とした連続講演を行い，非コンパクト対称空間内の部分多様体に関する有益な議論をすることができた。また3月には現地の若手研究者が来日し，広島大学で受け入れた。特に放物型部分群の Langlands 分解の可解部分の幾何学的な性質について議論を行い，現在も共同研究が進行中である。

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

特別な左不変リーマン計量の存在・非存在を決定づけるような不変量の構成までは至っていないが，その部分的な解答を与えることはできた。また，部分多様体に関しては，現在さまざまな研究が進行中である。さらに，左不変リーマン計量以外の幾何構造として，左不変な擬リーマン計量やシンプレクティック構造の研究も進行中である。いずれも論文としてまとめるところまでは至っていないが，部分的な結果は得られており，おおむね順調に進展していると判断する。

Strategy for Future Research Activity

すでに研究に取り掛かっている，非コンパクト対称空間への余等質性１作用の研究，放物型部分群の可解部分の幾何学的性質に関する研究，左不変擬リーマン計量の研究，左不変シンプレクティック構造の研究を，研究協力者達と共同で同時進行で推進する。それとともに，リー代数の不変量の構成を目指した研究も行いたい。

Research Products

• [Int'l Joint Research] Chonnam National University(韓国)
• [Int'l Joint Research] Universidade de Santiago de Compostela(スペイン)
• [Int'l Joint Research] Chonnam National University(韓国)
• [Int'l Joint Research] King's College London(イギリス)
• [Int'l Joint Research] King's College London(イギリス)
• [Int'l Joint Research] Chonnam National University(韓国)
• [Journal Article] Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces (2018)
  • Author(s): Jong Taek Cho, Takahiro Hashinaga, Akira Kubo, Yuichiro Taketomi, Hiroshi Tamaru
  • Journal Title: Journal of Geometry and Physics Volume: 123 Pages: 221-234
  • DOI: 10.1016/j.geomphys.2017.08.013
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On the nonexistence of left-invariant Ricci solitons --- a conjecture and examples (2018)
  • Author(s): Yuichiro Taketomi, Hiroshi Tamaru
  • Journal Title: Transformation Groups Volume: 23
  • DOI: 10.1007/s00031-017-9439-4
  • Peer Reviewed
• [Journal Article] Three-dimensional solvsolitons and the minimality of the corresponding submanifolds (2017)
  • Author(s): Takahiro Hashinaga, Hiroshi Tamaru
  • Journal Title: International Journal of Mathematics Volume: 28 Pages: 1750048-1750048
  • DOI: 10.1142/s0129167x17500483
  • Peer Reviewed
• [Journal Article] The Solvable Models of Noncompact Real Two-Plane Grassmannians and Some Applications (2017)
  • Author(s): Jong Taek Cho, Takahiro Hashinaga, Akira Kubo, Yuichiro Taketomi, Hiroshi Tamaru
  • Journal Title: Hermitian-Grassmannian Submanifolds, Springer Proc. Math. Stat. Volume: 203
  • DOI: 10.1007/978-981-10-5556-0_26
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Some conjectures concerning irreducible components of harmonic polynomials in the case of so(d,2) (2017)
  • Author(s): R. Wada, Y. Agaoka
  • Journal Title: Series of Monographs of Contemporary Social Systems Solutions Volume: 9
  • Peer Reviewed
• [Journal Article] Abundance of nilpotent orbits in real semisimple Lie algebras (2017)
  • Author(s): Takayuki Okuda
  • Journal Title: J. Math. Sci. Univ. Tokyo Volume: 24
  • NAID: 120006489989
  • Peer Reviewed
• [Journal Article] Geodesics of Riemannian symmetric spaces included in reflective submanifolds (2017)
  • Author(s): Takayuki Okuda
  • Journal Title: Contemporary Perspectives in Differential Geometry and its Related Fields Volume: なし
  • Peer Reviewed
• [Journal Article] Geodesics of Riemannian symmetric spaces included in reflective submanifolds (2017)
  • Author(s): Takayuki Okuda
  • Journal Title: Proceedings of the 5th International Colloquium on Differential Geometry and its Related Fields Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Type-changing PDE and singularities of Monge characteristic systems (2017)
  • Author(s): Noda, T. and Shibuya, K.
  • Journal Title: Advanced Studies in Pure Math. Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Milnor-type theorems for left-invariant Riemannian metrics on Lie groups (2016)
  • Author(s): Takahiro Hashinaga, Hiroshi Tamaru, Kazuhiro Terada
  • Journal Title: J. Math. Soc. Japan Volume: 68 Issue: 2 Pages: 669-684
  • DOI: 10.2969/jmsj/06820669
  • NAID: 130006887138
  • Peer Reviewed
• [Journal Article] On classification of quandles of cyclic type (2016)
  • Author(s): Seiichi Kamada, Hiroshi Tamaru, Koshiro Wada
  • Journal Title: Tokyo J. Math. Volume: 39 Pages: 157-171
  • DOI: 10.3836/tjm/1459367262
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The space of left-invariant Riemannian metrics (2016)
  • Author(s): Hiroshi Tamaru
  • Journal Title: Geometry and Topology of Manifolds, Springer Proc. Math. Stat. Volume: 154 Pages: 315-326
  • DOI: 10.1007/978-4-431-56021-0_17
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Flat connected finite quandles (2016)
  • Author(s): Yoshitaka Ishihara, Hiroshi Tamaru
  • Journal Title: Proc. Amer. Math. Soc. Volume: 144 Pages: 4959-4971
  • DOI: 10.1090/proc/13095
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Homogeneous Ricci soliton hypersurfaces in the complex hyperbolic spaces (2016)
  • Author(s): Takahiro Hashinaga, Akira Kubo, Hiroshi Tamaru
  • Journal Title: Tohoku Math. J. Volume: 68 Pages: 559-568
  • DOI: 10.2748/tmj/1486177215
  • Peer Reviewed
• [Journal Article] On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups (2016)
  • Author(s): Akira Kubo, Kensuke Onda, Yuichiro Taketomi, Hiroshi Tamaru
  • Journal Title: Hiroshima Math. J. Volume: 46
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Proper SL(2,R)-actions on homogeneous spaces (2016)
  • Author(s): Maciej Bochenski, Piotr Jastrzebski, Takayuki Okuda, Aleksy Tralle
  • Journal Title: Internat. J. Math. Volume: 27 Pages: 1650106-10
  • DOI: 10.1142/s0129167x16501068
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Homogeneous Ricci soliton hypersurfaces in the complex hyperbolic spaces (2016)
  • Author(s): Takahiro Hashinaga, Akira Kubo, Hiroshi Tamaru
  • Journal Title: Tohoku Math. J. Volume: 印刷中
  • Peer Reviewed
• [Journal Article] The space of left-invariant Riemannian metrics (2016)
  • Author(s): Hiroshi Tamaru
  • Journal Title: Geometry and Topology of Manifolds, Springer Proceedings in Mathematics & Statistics Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Homogeneous space with non-virtually abelian discontinuous groups but without any proper SL(2,R)-action (2016)
  • Author(s): Takayuki Okuda
  • Journal Title: Internat. J. Math. Volume: 27 Pages: 1650018-1650018
  • DOI: 10.1142/s0129167x1650018x
  • Peer Reviewed
• [Journal Article] Some remarks on cubature formulas with linear operators (2016)
  • Author(s): Masatake Hirao, Takayuki Okuda, Masanori Sawa
  • Journal Title: J. Math. Soc. Japan Volume: 68 Issue: 2 Pages: 711-735
  • DOI: 10.2969/jmsj/06820711
  • NAID: 130006887144
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4 (2016)
  • Author(s): Takayuki Okuda, Wei-Hsuan Yu
  • Journal Title: European J. Combin. Volume: 53
  • DOI: 10.1016/j.ejc.2015.11.003
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Explicit irreducible decomposition of harmonic polynomials in the case of so(p,2) (2016)
  • Author(s): R. Wada, Y. Agaoka
  • Journal Title: Contemporary Works in Economic Sciences Volume: 7
  • Peer Reviewed
• [Journal Article] Heesch 数について --- タイリングできないタイル (2016)
  • Author(s): 阿賀岡芳夫
  • Journal Title: 研究会「直観幾何学２０１６」講演アブストラクト Volume: なし
• [Journal Article] A variational problem for curves on Riemann-Finsler surfaces (2016)
  • Author(s): Sabau, S.V., Shibuya, K.
  • Journal Title: J. Aust. Math. Soc. Volume: 印刷中
  • Peer Reviewed
• [Journal Article] The space of left-invariant Riemannian metrics (2016)
  • Author(s): Hiroshi Tamaru
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Moment maps and isoparametric hypersurfaces in spheres--Hermitian cases (2015)
  • Author(s): Shinobu Fujii, Hiroshi Tamaru
  • Journal Title: Transf. Groups Volume: 印刷中 Pages: 417-436
  • DOI: 10.1007/s00031-015-9305-1
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 対称空間論の離散化とカンドル代数, Part II (2015)
  • Author(s): Hiroshi Tamaru
  • Journal Title: 研究集会「部分多様体論・湯沢 2014」記録集 Volume: 無
• [Journal Article] Naturally reductive homogeneous real hypersurfaces in a nonflat complex space form (2015)
  • Author(s): Sadahiro Maeda, Hiroshi Tamaru
  • Journal Title: Topology Appl. Volume: 196 Pages: 675-683
  • DOI: 10.1016/j.topol.2014.01.020
  • Peer Reviewed
• [Journal Article] Smallest complex nilpotent orbits with real points (2015)
  • Author(s): Takayuki Okuda
  • Journal Title: J. Lie Theory Volume: 25
  • Peer Reviewed
• [Journal Article] Spherical designs of harmonic index t (2015)
  • Author(s): Eiichi Bannai, Takayuki Okuda, Makoto Tagami
  • Journal Title: J. Approx. Theory Volume: 195 Pages: 1-18
  • DOI: 10.1016/j.jat.2014.06.010
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] リーマン対称空間中の全測地的曲面と冪零軌道 (2015)
  • Author(s): 久保亮, 間下克哉, 奥田隆幸, 田丸博士
  • Journal Title: 研究集会「部分多様体幾何とリー群作用 2015」予稿集 Volume: なし
• [Journal Article] 曲面群と同型な基本群を持つ擬リーマン局所対称空間について (2015)
  • Author(s): 奥田隆幸
  • Journal Title: 研究集会「リーマン面に関連する位相幾何学」予稿集 Volume: なし
• [Journal Article] アソシエーションスキームの商集合についての Delsarte 理論 (2015)
  • Author(s): 奥田隆幸
  • Journal Title: 第32回代数的組合せ論シンポジウム講究録 Volume: なし
• [Journal Article] 対称空間論の離散化とカンドル代数, Part I (2015)
  • Author(s): 田丸 博士
  • Journal Title: Geometry and Analysis (福岡大学微分幾何研究会 2014 記録集) Volume: 1 Pages: 99-107
  • Acknowledgement Compliant
• [Journal Article] Naturally reductive homogeneous real hypersurfaces in a nonflat complex space form (2015)
  • Author(s): Sadahiro Maeda, Hiroshi Tamaru
  • Journal Title: Topology Appl. (Special Issues) Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Milnor-type theorems for left-invariant Riemannian metrics on Lie groups (2015)
  • Author(s): Takahiro Hashinaga, Hiroshi Tamaru, Kazuhiro Terada
  • Journal Title: J. Math. Soc. Japan Volume: 印刷中
  • NAID: 130006887138
  • Peer Reviewed
• [Journal Article] 対称空間論の離散化とカンドル代数, Part II (2015)
  • Author(s): 田丸 博士
  • Journal Title: 研究集会「部分多様体論・湯沢 2014」記録集 Volume: 19
  • Open Access
• [Journal Article] On totally geodesic surfaces in symmetric spaces of type AI (2014)
  • Author(s): Takuya Fujimaru, Akira Kubo, Hiroshi Tamaru
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 106 Pages: 211-227
  • DOI: 10.1007/978-4-431-55215-4_19
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Group actions on symmetric spaces related to left-invariant geometric structures (2014)
  • Author(s): Hiroshi Tamaru
  • Journal Title: RIMS Kokyuroku Volume: 1929 Pages: 1-12
  • Open Access / Acknowledgement Compliant
• [Journal Article] Generalized Finsler structures on closed 3-manifolds (2014)
  • Author(s): Sorin V. Sabau, Kazuhiro Shibuya, Gheorghe Pitis
  • Journal Title: Tohoku Math. J. (2) Volume: 66 Pages: 321-353
  • DOI: 10.2748/tmj/1412783202
  • Peer Reviewed
• [Journal Article] Metric structures associated to Finsler metrics (2014)
  • Author(s): Sorin V. Sabau, Kazuhiro Shibuya, Hideo Shimada
  • Journal Title: Publ. Math. Debrecen Volume: 84 Pages: 89-103
  • Peer Reviewed
• [Presentation] Left-invariant pseudo-Riemannian metrics on some solvable Lie groups (2018)
  • Author(s): Hiroshi Tamaru
  • Organizer: AMS Special Session on Nilpotent and Solvable Geometry
  • Int'l Joint Research / Invited
• [Presentation] Flat quandles and finite subsets in symmetric spaces (2018)
  • Author(s): Hiroshi Tamaru
  • Organizer: Hakata Workshop Winter Meeting 2018: Discrete Mathematics and its Applications
  • Invited
• [Presentation] Left-invariant pseudo-Riemannian metrics on some Lie groups (2018)
  • Author(s): Hiroshi Tamaru
  • Organizer: Geometry of Submanifolds and Integrable Systems
  • Int'l Joint Research / Invited
• [Presentation] Left-invariant metrics and submanifold geometry (2017)
  • Author(s): Hiroshi Tamaru
  • Organizer: Lie Group Actions in Riemannian Geometry
  • Int'l Joint Research / Invited
• [Presentation] Symmetric spaces, submanifold geometry, and solvmanifolds (2017)
  • Author(s): Hiroshi Tamaru
  • Organizer: Capital Normal University-Hiroshima University Joint Conference on Mathematics
  • Int'l Joint Research / Invited
• [Presentation] 3次元リーマン多様体が4次元ユークリッド空間へ局所等長埋め込み可能となるための必要十分条件 (2017)
  • Author(s): 阿賀岡芳夫, 橋永貴弘
  • Organizer: 日本数学会
  • Place of Presentation: 首都大学東京
• [Presentation] カンドルにおける平坦性と可換性 (2017)
  • Author(s): 田丸博士
  • 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
  • Invited
• [Presentation] Left-invariant metrics and submanifold geometry (2017)
  • Author(s): Hiroshi Tamaru
  • Organizer: The 7th International Workshop on Differential Geometry
  • Place of Presentation: 虹ノ松原ホテル
  • Int'l Joint Research / Invited
• [Presentation] Quandles and discrete symmetric spaces --- flatness and commutativity (2017)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Ricci soliton and contact homogeneous hypersurfaces in noncompact symmetric spaces (2017)
  • Author(s): Hiroshi Tamaru
  • Organizer: Workshop on Differential Geometry, Gwangju-2017
  • Place of Presentation: Chonnam National University, 韓国
  • Int'l Joint Research / Invited
• [Presentation] リーマン対称空間内の測地線を共有しない全測地的部分多様体の組について (2017)
  • Author(s): 奥田隆幸
  • Organizer: 日本数学会2017年度会, 幾何学分科会特別講演
  • Place of Presentation: 首都大学東京
  • Invited
• [Presentation] Delsarte theory on compact symmetric spaces (2017)
  • Author(s): Takayuki Okuda
  • Organizer: Japan-Korea workshop on algebra and combinatorics
  • Place of Presentation: 熊本大学
  • Int'l Joint Research / Invited
• [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 (2016)
  • Author(s): 田丸博士
  • Organizer: 北九州数理科学セミナー
  • Place of Presentation: 北九州高等専門学校
  • Invited
• [Presentation] On totally geodesic surfaces in symmetric spaces and applications (2016)
  • Author(s): Hiroshi Tamaru
  • Organizer: Japan-China Geometry Conference
  • Place of Presentation: 福建師範大学, 中国
  • 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 overview (2016)
  • Author(s): 田丸博士
  • Organizer: 合宿セミナー 2016 in 山口
  • Place of Presentation: 山口紅花舎
• [Presentation] Left-invariant metrics and submanifold geometry (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Structures of association schemes on great antipodal sets of Hermitian symmetric spaces (2016)
  • Author(s): Takayuki Okuda, Hirotake Kurihara
  • Organizer: RIMS Workshop: Research on Finite Groups, Algebraic Combinatorics and Vertex Operator Algebras
  • Place of Presentation: 京都大学
  • Int'l Joint Research / Invited
• [Presentation] Delsarte theory for quotients of association schemes (2016)
  • Author(s): Takayuki Okuda
  • Organizer: International Workshop of Algebraic Combinatorics
  • Place of Presentation: Anhui University, 中国
  • Int'l Joint Research
• [Presentation] Totally geodesic submanifolds of Riemmaninan symmetric spaces and proper actions of reductive group on Pseudo-Riemannian symmetric spaces (2016)
  • Author(s): Takyuki Okuda
  • Organizer: The fifth International Colloquium of Differential Geometry and it's Related Fields 2016
  • Place of Presentation: Veliko Tarnovo, Bulgaria
  • Int'l Joint Research / Invited
• [Presentation] Hermite 対称空間内の全測地的複素曲線 (2016)
  • Author(s): 久保亮, 奥田隆幸, 田丸博士
  • Organizer: 日本数学会2016年度秋季総合分科会
  • Place of Presentation: 関西大学
• [Presentation] A classification problem for 3rd order PDEs via differential systems (2016)
  • Author(s): Kazuhiro Shibuya
  • Organizer: The second China-Japan geometry conference
  • Place of Presentation: Fuzhou, China
  • Int'l Joint Research / Invited
• [Presentation] A classification problem for 3rd order PDEs via differential systems (2016)
  • Author(s): Kazuhiro Shibuya
  • Organizer: The 51-th Symposium on Finsler Geometry
  • Place of Presentation: Kagoshima
  • Int'l Joint Research / Invited
• [Presentation] A classification problem for 3rd order PDEs via differential systems (2016)
  • Author(s): Kazuhiro Shibuya
  • Organizer: Geometry Seminar in Northeast Normal University
  • Place of Presentation: Changchun, China
  • Int'l Joint Research / Invited
• [Presentation] Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces (2016)
  • Author(s): Hiroshi Tamaru
  • Organizer: The 11th OCAMI-RIRCM Joint Differential Geometry Workshop on Submanifolds and Lie Theory
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2016-03-21
  • Int'l Joint Research / Invited
• [Presentation] On totally geodesic surfaces in symmetric spaces and applications (2016)
  • Author(s): Hiroshi Tamaru
  • Organizer: Workshop in honor of Professor Hiroo Naitoh's retirement
  • Place of Presentation: 山口大学
  • Year and Date: 2016-03-05
  • Int'l Joint Research / Invited
• [Presentation] 対称空間論の離散化とカンドル代数 (2015)
  • Author(s): Hiroshi Tamaru
  • Organizer: 大阪大学数学教室談話会
  • Place of Presentation: 大阪大学
  • Year and Date: 2015-12-07
• [Presentation] Milnor-type theorems for left-invariant metrics (2015)
  • Author(s): Hiroshi Tamaru
  • Organizer: 筑波大学微分幾何学火曜セミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2015-10-27
• [Presentation] The space of left-invariant metrics and submanifold geometry (2015)
  • Author(s): Hiroshi Tamaru
  • Organizer: AMS Special Session on Ricci Curvature for Homogeneous Spaces and Related Topics
  • Place of Presentation: San Antonio (Texas, USA)
  • Year and Date: 2015-01-10
  • Invited
• [Presentation] Quandles and a discretization of the theory of symmetric spaces (2014)
  • Author(s): 田丸 博士
  • Organizer: 部分多様体論・湯沢2014
  • Place of Presentation: 湯沢グランドホテル (新潟県)
  • Year and Date: 2014-11-22
  • Invited
• [Presentation] 対称空間論の離散化とカンドル代数 (2014)
  • Author(s): 田丸 博士
  • Organizer: 上智大学談話会
  • Place of Presentation: 上智大学
  • Year and Date: 2014-11-07
  • Invited
• [Presentation] 対称空間論の離散化とカンドル代数 (2014)
  • Author(s): 田丸 博士
  • Organizer: 福岡大学微分幾何研究会
  • Place of Presentation: 福岡大学セミナーハウス
  • Year and Date: 2014-11-01
  • Invited
• [Presentation] The space of left-invariant metrics (2014)
  • Author(s): Hiroshi Tamaru
  • Organizer: The 10th Geometry Conference for the Friendship between China and Japan
  • Place of Presentation: Fudan University (China)
  • Year and Date: 2014-09-11
  • Invited
• [Presentation] On totally geodesic surfaces in symmetric spaces of type AI (2014)
  • Author(s): Hiroshi Tamaru
  • Organizer: ICM 2014 Satellite Conference on Real & Complex Submanifold
  • Place of Presentation: NIMS (Korea)
  • Year and Date: 2014-08-11
  • Invited
• [Presentation] Group actions on symmetric spaces related to left-invariant geometric structures (2014)
  • Author(s): Hiroshi Tamaru
  • Organizer: Development of group actions and submanifold theory
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-06-25
  • Invited
• [Presentation] An interaction between geometry of left-invariant metrics and group actions on symmetric spaces (2014)
  • Author(s): Hiroshi Tamaru
  • Organizer: Submanifold Geometry and Related Topics
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2014-04-14
  • Invited
• [Book] Challenging Researches in Economic Sciences: Legal Informatics, Environmental Economics, Economics, OR and Mathematics (2017)
  • Author(s): M. Kitahara, C. Czerkawski, O. Kurihara, H. Hasegawa, S. Sakai, T. Takahara, R. Wada, Y. Agaoka, A. Kubo
  • Total Pages: 141
  • Publisher: Kyushu Univ. Press
• [Book] New Solutions in Legal Informatics, Economic Sciences and Mathematics (2015)
  • Author(s): M. Kitahara, T. Ogawa, K. Iyori, T. Yano, H. Kosaka, M. Sakaguchi, M. Kodama, S. Sakai, T. Takahama, R. Wada, Y. Agaoka
  • Total Pages: 152
  • Publisher: Kyushu University Press
• [Remarks] Tamaru's WEB PAGE
  • URL: http://www.math.sci.hiroshima-u.ac.jp/~tamaru/index-j.html
• [Funded Workshop] Workshop in honor of Professor Hiroo Naitoh's retirement (2016)
  • Place of Presentation: 山口大学
  • Year and Date: 2016-03-05