Kobayashi-Hitchin correspondence for polarized algebraic manifolds and Kahler-Ricci flows

• Project/Area Number: 20540069
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Kanazawa University
• Principal Investigator: NAKAGAWA Yasuhiro Kanazawa University, 数物科学系, 准教授 (90250662)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: Einstein-Kahler計量 / 幾何学的不変式論 / 安定性 / Einstein-佐々木計量 / Einstein・Kahler計量 / 二木指標 / Einstein・佐々木計量 / Kahler・Ricciソリトン

Research Abstract

Firstly, we have generalized the notion of Kahler-Ricci solitons to the case of general polarized manifolds, which are called" generalized Kahler-Ricci solitons". Moreover, we have constructed a non-trivial example of a generalieze Kahler-Ricci soliton. Next, we have constructed new examples of non-toric Einstein-Sasaki manifolds, that is, we have constructed Einstein-Sasaki metrics on certain unit-circle bundles associated to the canonical line bundles of projective line-bundles over Kahler-Einstein Fano manifolds

Research Products

• [Journal Article] On generalized Kahler-Ricci solitons (2011)
  • Author(s): Y. Nakagawa
  • Journal Title: Osaka J. Math Volume: 48 Pages: 497-513
  • Peer Reviewed
• [Journal Article] On generalized Kahler-Ricci solitons (2011)
  • Author(s): Y.Nakagawa
  • Journal Title: Osaka J.Math. 掲載予定. Pages: 48-48
  • Peer Reviewed
• [Journal Article] On generalized Kahler-Ricci solitons (2011)
  • Author(s): Yasuhir Nakagawa
  • Journal Title: Osaka Journal of Mathematics Volume: 48(掲載確定)
  • Peer Reviewed
• [Journal Article] On generalized Kahler-Ricci solitons (2010)
  • Author(s): Yasuhir Nakagawa
  • Journal Title: Osaka Journal of Mathematics (in press)
  • Peer Reviewed
• [Presentation] New examples of Sasaki-Einstein manifolds (2011)
  • Author(s): 中川泰宏
  • Organizer: Seminar on Complex Manifolds in Kumamoto
  • Place of Presentation: 熊本大学(熊本県)
  • Year and Date: 2011-01-11
• [Presentation] New examples of Sasaki-Einstein manifolds (2011)
  • Author(s): 中川泰宏
  • Organizer: Seminar on Complex Manifolds in Kumamoto
  • Place of Presentation: 熊本大学(熊本県).
  • Year and Date: 2011-01-11
• [Presentation] New examples of Sasaki-Einstein manifolds (2010)
  • Author(s): 中川泰宏
  • Organizer: The 16th International Symposium on Complex Geometry
  • Place of Presentation: 信州菅平プチホテルゾンタック(長野県)
  • Year and Date: 2010-10-20
• [Presentation] New examples of Sasaki-Einstein manifolds (2010)
  • Author(s): 中川泰宏
  • Organizer: The 16th International Symposium on Complex Geometry
  • Place of Presentation: 信州菅平 プチホテルゾンタック(長野県).
  • Year and Date: 2010-10-20
• [Presentation] New examples of Sasaki-Einstein manifolds (2010)
  • Author(s): 中川泰宏
  • Organizer: The 16th International Symposium on Complex Geomery
  • Place of Presentation: 信州菅平高原ゾチホテルゾンタツク(招待講演)
  • Year and Date: 2010-10-20
• [Presentation] Kahler・Ricci ソリトンの一般化について (その2) (2009)
  • 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 (福岡県)
  • Year and Date: 2009-11-22
• [Presentation] Generalized Kaehler-Ricciソリトンについて (2008)
  • Author(s): 中川泰宏
  • Organizer: 幾何学阿蘇研究集会
  • Place of Presentation: 休暇村南阿蘇
  • Year and Date: 2008-09-02