Research of nice bounded realizations of homogeneous bounded domains and their applications to Kaehler manifolds

• Project/Area Number: 20840018
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kanazawa University
• Principal Investigator: KAI Chifune Kanazawa University, 数物科学系, 助教 (70506815)
• Project Period (FY): 2008 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,276,000 (Direct Cost: ¥2,520,000、Indirect Cost: ¥756,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2008: ¥1,716,000 (Direct Cost: ¥1,320,000、Indirect Cost: ¥396,000)
• Keywords: 等質有界領域 / ケイリー変換 / 代表領域 / 等質錐 / 因果構造 / シーゲル領域 / ジーゲル領域 / ベルグマン核 / 勾配写像

Research Abstract

上半平面の一般化である等質ジーゲル領域は、ケイリー変換によってある有界領域に双正則に写される。このケイリー変換の像が、ベルグマンによって導入された代表領域と一致することを証明した。またジーゲル領域の定義に現れる錐について、錐の各点で過去・未来の方向を指定する因果構造の研究を行った。その結果、対称錐の一種であるローレンツ錐に対して、その因果構造を保つ自己同型が線型であるという定理の、初等的な証明を得た。

Research Products

• [Journal Article] The representative domain of a homogeneous bounded domain (2010)
  • Author(s): Ishi, H., Kai, C.
  • Journal Title: Kyushu Journal of Mathematics 64 Pages: 35-47
  • NAID: 130000259012
  • Peer Reviewed
• [Journal Article] The representative domain of a homogeneous bounded domain (2010)
  • Author(s): H.Ishi, C.Kai
  • Journal Title: Kyushu Journal of Mathematics 64 Pages: 35-47
  • NAID: 130000259012
  • Peer Reviewed
• [Journal Article] A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps (2008)
  • Author(s): Kai, C.
  • Journal Title: Journal of the Mathematical Society of Japan 60 Pages: 1107-1134
  • NAID: 10024905327
  • Peer Reviewed
• [Journal Article] A characterization of symmetr ic cones by an order-reversing property of the pseudoinverse maps (2008)
  • Author(s): Chifune Kai
  • Journal Title: Journal of the Mathemat ical Society of Japan 60 Pages: 1107-1134
  • Peer Reviewed
• [Presentation] An elementary proof of the linearity of causal automorphims of 3-dimensional Lorentz cone (2009)
  • Author(s): 甲斐千舟
  • Organizer: 2009年度表現論ワークショップ
  • Place of Presentation: とりぎん文化会館(鳥取県)
  • Year and Date: 2009-12-26
• [Presentation] The representative domain of a homogeneous bounded domain (2009)
  • Author(s): Kai, C.
  • Organizer: JSPS-MHESRT Seminar: "Geometric and Harmonic Analysis on Homogeneous Spaces"
  • Place of Presentation: Le Grand Hotel of Kerkennah (Tunisia)
  • Year and Date: 2009-11-06
• [Presentation] The representative domain of a homogeneous bounded domain (2009)
  • Author(s): C.Kai
  • Organizer: JSPS-MHESRT Seminar : "Geometric and Harmonic Analysis on Homogeneous Spaces"
  • Place of Presentation: Le Grand Hotel of Kerkennah(Tunisia)
  • Year and Date: 2009-11-06
• [Presentation] A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps (2008)
  • Author(s): Kai, C.
  • Organizer: JSPS-RFBR Workshop "Harmonic Analysis on Homogeneous Spaces and Quantization"
  • Place of Presentation: 東京大学玉原国際セミナーハウス(群馬県)
  • Year and Date: 2008-08-25
• [Presentation] A note on the Bergman metric of bounded homogeneous domains (2008)
  • Author(s): Kai, C.
  • Organizer: International Workshop "Problems related to Bergman kernel"
  • Place of Presentation: 中国科学院数学与系統科学研究院・数学研究所(中国)
  • Year and Date: 2008-06-12
• [Presentation] A note on the Bergman metric of bounded homogeneous domains (2008)
  • Author(s): Chifune Kai
  • Organizer: International Workshop "Problems Related to Bergman kernel"
  • Place of Presentation: 中国科学院数学研究所(中国・北京)
  • Year and Date: 2008-06-12