Characterizations of complex manifolds by means of holomorphic automorphism groups

• Project/Area Number: 24540166
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kanazawa University
• Principal Investigator: KODAMA Akio 金沢大学, 数物科学系, 教授 (20111320)
• Co-Investigator(Kenkyū-buntansha): SHIMIZU Satoru 東北大学, 大学院理学研究科, 准教授 (90178971)
• Co-Investigator(Renkei-kenkyūsha): KASUE Atsushi 金沢大学, 数物科学系, 教授 (40152657)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 正則自己同型群 / 一般複素楕円型領域 / 一般型ハルトークスの三角形 / ラインハルト領域 / リュービル葉層構造 / 一般ハルトークスの三角形 / 国際情報交換

Outline of Final Research Achievements

The main purpose of this research is to determine the complex manifold structure by means of the topological group structure of its holomorphic automorphism group. This is very difficult and this cannot be achieved in full generality at this moment. However, we could determine completely the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles. Also, we obtained some important fundamental results on unbounded Reinhardt domains.

Research Products

• [Journal Article] On the holomorphic automorphism group of a generalized Hartogs triangle (2015)
  • Author(s): Akio Kodama
  • Journal Title: Tohoku Math. J. Volume: 未定
  • NAID: 130008106071
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Holomorphic equivalence problem for Reinhardt domains and the conjugacy of torus actions (2015)
  • Author(s): Satoru Shimizu
  • Journal Title: Tohoku Math. J. Volume: 未定
  • NAID: 130008106145
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On the holomorphic automorphism group of a generalized complex ellipsoid (2014)
  • Author(s): Akio Kodama
  • Journal Title: Complex Variables and Elliptic Equations Volume: 59 Issue: 9 Pages: 1342-1349
  • DOI: 10.1080/17476933.2013.845177
  • NAID: 120005463330
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Homogeneous Reinhardt domains containing no coordinate hyperplanes (2014)
  • Author(s): Satoru Shimizu and Kouichi Kimura
  • Journal Title: Kodai Math. J. Volume: 37
  • NAID: 130004496209
  • Peer Reviewed
• [Journal Article] Diffeomorphisms between Siegel domains of the first kind preserving the holomorphic automorphism groups and applications (2013)
  • Author(s): Akio Kodama and Satoru Shimizu
  • Journal Title: Kodai Math. J. Volume: 36
  • NAID: 130004687987
  • Peer Reviewed
• [Journal Article] Prolongation of holomorphic vector fields on a tube domain (2013)
  • Author(s): Satoru Shimizu
  • Journal Title: Tohoku Math. J. Volume: 65
  • NAID: 130005585320
  • Peer Reviewed
• [Journal Article] Diffeomorphisms between Siegel domains of the first kind preserving the holomorphic automorhism groups and applications (2013)
  • Author(s): Akio Kodama and Satoru Shimizu
  • Journal Title: Kodai Math. J. Volume: 印刷中
  • Peer Reviewed
• [Presentation] 正則自己同型群に関連するいくつかの問題 (2015)
  • Author(s): 児玉秋雄
  • Organizer: 金沢大学数理学談話会
  • Place of Presentation: 金沢大学
  • Year and Date: 2015-03-27
• [Presentation] On the holomorphic automorphism group of a generalized Hartogs triangle and a related question (2015)
  • Author(s): 児玉秋雄
  • Organizer: 日本数学会年会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-24
• [Presentation] 原点を含むある種の非有界ラインハルト領域に関する正則同値問題 (2014)
  • Author(s): 清水悟
  • Organizer: 多変数関数論冬セミナー
  • Place of Presentation: 金沢大学
  • Year and Date: 2014-12-21
  • Invited
• [Presentation] On the holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (2014)
  • Author(s): 児玉秋雄
  • Organizer: 函数論シンポジウム
  • Place of Presentation: 東北大学
  • Year and Date: 2014-11-08
  • Invited
• [Presentation] 原点を含むある種の非有界ラインハルト領域に関する正則同値問題 (2014)
  • Author(s): 清水悟
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-25
• [Presentation] Some results on Siegel domains of the first kind with isomorphic automorphism groups (2012)
  • Author(s): Akio Kodama
  • Organizer: The 20th International Coference on Finite or Infinite Dimensional Complex Analysisi and Applications
  • Place of Presentation: Hanoi University of Science and Technology
  • Invited
• [Presentation] On the holomorphic automorphism group of a generalized complex ellipsoid
  • Author(s): 児玉秋雄
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 愛媛大学
• [Presentation] On the holomorphic automorphism group of a generalized complex ellipsoid
  • Author(s): 児玉秋雄
  • Organizer: 東北複素解析セミナー
  • Place of Presentation: 東北大学
• [Presentation] 多変数複素解析における特殊領域
  • Author(s): 清水悟
  • Organizer: 日本数学会年会
  • Place of Presentation: 学習院大学
  • Invited
• [Presentation] Diffeomorphisms between Siegel domains of the first kind preserving the holomorphic automorhism groups and applications
  • Author(s): Akio Kodama
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
• [Presentation] Diffeomorphisms between Siegel domains of the first kind preserving the holomorphic automorhism groups and applications
  • Author(s): Akio Kodama
  • Organizer: 多変数関数論冬セミナー
  • Place of Presentation: 東北大学
  • Invited