Kaehler-Ricci flows and the stability for polarized algebraic manifolds

• Project/Area Number: 23540080
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Saga University (2012-2014); Kanazawa University (2011)
• Principal Investigator: NAKAGAWA Yasuhiro 佐賀大学, 工学(系)研究科(研究院), 教授 (90250662)
• Project Period (FY): 2011-04-28 – 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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: Einstein・Kaehler 計量 / 幾何学的不変式論 / 安定性 / Kaehler・Ricci ソリトン / Kaehler・Ricci 流 / Kaehler・Ricc ソリトン / Kaehler・Ricc 流

Outline of Final Research Achievements

Firstly, we have generalized the notion of Kaehler-Ricci solitons to the case of general polarized manifolds, which are called “generalized Kaehler-Ricci solitons”. Moreover, we have constructed a non-trivial example of a generaliezed Kaehler-Ricci soliton. Secondary, we have constructed new examples of non-toric Einstein-Sasaki manifolds. Thirdly, we have constructed higher dimensional generalizations of exmaples, due to Nill and Paffenholz, of non-symmetric Einstein-Kaehler toric Fano manofolds.

Research Products

• [Journal Article] On the examples of Nill and Paffenholz (2015)
  • Author(s): Yasuhiro Nakagawa
  • Journal Title: International Journal of Mathematics Volume: 未定
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] New examples of Sasaki-Einstein manifolds (2013)
  • Author(s): Toshiki Mabuchi and Yasuhiro Nakagawa
  • Journal Title: Tohoku Mathematical Journal Volume: 65 Pages: 243252-243252
  • NAID: 130005562143
  • Peer Reviewed
• [Journal Article] On generalized Kaehler-Ricci solitons (2011)
  • Author(s): Yasuhiro Nakagawa
  • Journal Title: Osaka Journal of Mathematics Volume: 48
  • Peer Reviewed
• [Presentation] Nill・Paffenholz の例の一般化について (2015)
  • Author(s): 中川 泰宏
  • Organizer: 満渕俊樹教授 退職記念 小研究会
  • Place of Presentation: 大阪大学 理学部
  • Year and Date: 2015-03-12 – 2015-03-13
  • Invited
• [Presentation] Nill・Paffenholz の例の一般化について (2015)
  • Author(s): 中川 泰宏
  • Organizer: 淡路島幾何学研究集会 2015
  • Place of Presentation: 淡路島 国民宿舎 慶野松原荘
  • Year and Date: 2015-01-23 – 2015-01-25
  • Invited
• [Presentation] Nill・Paffenholz の例について (その 2) (2014)
  • Author(s): 中川 泰宏
  • 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: 2014-10-31 – 2014-11-03
  • Invited
• [Presentation] Nill ・ Paffenholz の例の高次元化について (2014)
  • Author(s): 中川 泰宏
  • Organizer: 代数多様体とその周辺
  • Place of Presentation: 琉球大学理学部
  • Year and Date: 2014-09-29 – 2014-10-02
  • Invited
• [Presentation] On the examples of Nill-Paffenholz (2013)
  • Author(s): 中川 泰宏
  • Organizer: 第１９回複素幾何シンポジウム
  • Place of Presentation: 信州菅平高原 プチホテル ゾンタック
• [Presentation] Nill・Paffenholz の例について (2013)
  • Author(s): 中川 泰宏
  • 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
• [Presentation] 佐々木・Einstein 多様体の新しい例について (2012)
  • Author(s): 中川 泰宏
  • 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
  • Invited