The construction of canonical form theory in geometry

• Project/Area Number: 25400070
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto Institute of Technology
• Principal Investigator: Ikawa Osamu 京都工芸繊維大学, 基盤科学系, 教授 (60249745)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 対称三対 / 対称空間 / 超極作用 / 実形 / Hermann作用 / Ｈｅｒｍａｎｎ作用 / エルミート対称空間 / 複素旗多様体 / 標準形 / Hermite対称空間

Outline of Final Research Achievements

(1) For a given compact connected simple Lie group and an involution on it, we can define a hyperpolar action. The author studied the orbit space and the properties of each orbit of the action. The result is a natural extension of maximal torus theory.

(2) We studied the necessary and sufficient condition that two real forms in a Hermitian symmetric space of compact type intersect discretely. When the intersection is discrete we expressed the intersection as the orbit of a Weyl group which is defined by a symmetric triad. Moreover we generalized the result when the ambient space is a generalized flag manifold.

Research Products

• [Journal Article] The fixed point set of a holomorphic isometry, the intersection of two real forms in a Hermitian symmetric space of compact type (2015)
  • Author(s): O. Ikawa, M. S. Tanaka and H. Tasaki
  • Journal Title: International Journal of Mathematics Volume: 26 Issue: 06 Pages: 1-32
  • DOI: 10.1142/s0129167x15410050
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The fixed point set of a holomorphic isometry, the intersection of two real forms in a Hermitian symmetric space of compact type and symmetric triads (2015)
  • Author(s): Osamu Ikawa, Makiko Sumi Tanaka, Hiroyuki Tasaki
  • Journal Title: Global analysis and differential geometry on manifolds Volume: 26 Pages: 1-32
  • NAID: 120007136370
  • Peer Reviewed
• [Journal Article] The fixed point set of a holomorphic isometry and the intersection of two real forms in the complex Grassmann manifold (2014)
  • Author(s): O. Ikawa, M. S. Tanaka and H. Tasaki
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 106 Pages: 319-327
  • DOI: 10.1007/978-4-431-55215-4_28
  • ISBN: 9784431552147, 9784431552154
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Editor's Message to Special Issue on Theory and Application of Agent Research (2013)
  • Author(s): O.Ikawa and Shimabukuroe
  • Journal Title: Journal of Information Processing Volume: 21 Issue: 1 Pages: 1-1
  • DOI: 10.2197/ipsjjip.21.1
  • NAID: 130003369497
  • ISSN: 1882-6652
  • Peer Reviewed
• [Journal Article] A note on symmetric triad and Hermann action (2013)
  • Author(s): O. Ikawa
  • Journal Title: Differential geometry of submanifolds and its related topics, World Scientific Volume: 1 Pages: 220-229
  • Peer Reviewed
• [Journal Article] Canonical forms under certain actions on the classical compact simple Lie groups
  • Author(s): Osamu Ikawa
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 106 Pages: 329-338
  • DOI: 10.1007/978-4-431-55215-4_29
  • ISBN: 9784431552147, 9784431552154
  • Peer Reviewed
• [Presentation] 二つの佐武図形による重複度付き対称三対の決定 (2015)
  • Author(s): 井川 治
  • Organizer: 神楽坂幾何学セミナー
  • Place of Presentation: 東京理科大学（東京都新宿区)
  • Year and Date: 2015-12-05
• [Presentation] 複素旗多様体内の二つの実形の交叉 (2015)
  • Author(s): 奥田隆幸，井川治，入江博，酒井高司，田崎博之
  • Organizer: 日本数学会年会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-22
• [Presentation] コンパクトリー群へのある作用の標準形 (2015)
  • Author(s): 井川 治
  • Organizer: 研究集会「幾何構造の融合と発展」
  • Place of Presentation: 名城大学
  • Year and Date: 2015-03-10
• [Presentation] 対称三対の基礎と応用 (2014)
  • Author(s): 井川 治
  • Organizer: 日本数学会秋季総合分科会 幾何学分科会 特別講演
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-24 – 2014-09-28
  • Invited
• [Presentation] 対称三対の実形の交叉への応用 (2014)
  • Author(s): 井川 治
  • Organizer: 第61回幾何学シンポジウム
  • Place of Presentation: 名城大学
  • Year and Date: 2014-08-24
• [Presentation] Canonical forms under certain actions on the classical compact simple Lie groups (2014)
  • Author(s): Ｏ． Ｉｋａｗａ
  • Organizer: ICM Satellite conference
  • Place of Presentation: Ｋｏｒｅａ
  • Year and Date: 2014-08-10
• [Presentation] Symmetric riads and thier applications (2014)
  • Author(s): 井川治
  • Organizer: 研究集会
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-06-27
• [Presentation] 対称三対とその応用 (2014)
  • Author(s): 井川治
  • Organizer: 秋葉原微分幾何セミナー
  • Place of Presentation: 秋葉原
  • Year and Date: 2014-05-24
• [Presentation] 二つの実形の交叉と対称三対 (2013)
  • Author(s): 井川治
  • Organizer: 「部分多様体幾何とリー群作用」
  • Place of Presentation: 東京理科大学
• [Presentation] 正則等長変換の不動点集合、実形の交叉と対称三対 (2013)
  • Author(s): 井川治
  • Organizer: 部分多様体論・湯沢2013
  • Place of Presentation: 湯沢グランドホテル
• [Remarks] KIT研究者総覧
  • URL: http://www.research-db.jim.kit.ac.jp/kitdb/servlet/
• [Remarks] KIT研究者総覧
  • URL: http://www.research-db.jim.kit.ac.jp