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Studies on Kobayashi-Hitchin correspondence from the view point of Kahelre-Ricci flow

Research Project

Project/Area Number 15K04848
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKumamoto University (2019-2020)
Saga University (2015-2018)

Principal Investigator

Nakagawa Yasuhiro  熊本大学, 大学院先端科学研究部(理), 教授 (90250662)

Project Period (FY) 2015-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsEinstein・Kaehler計量 / Kaehler・Ricciソリトン / 満渕ソリトン / 安定性 / トーリックFano多様体 / KSM多様体 / Einstein・Kaehler 計量 / Kaehler・Ricci ソリトン / トーリック Fano 多様体 / 幾何学的不変式論 / Kaehlre・Ricci ソリトン
Outline of Final Research Achievements

We introduced the notion of KSM-manifold, which has the structure of a fiber bundle over an Einstein-Kaehler Fano manifold whose fiber is a toric Fano manifold, and proved that every KSM-manifold admits a Kaehler-Ricci soliton. In particular, by choosing a non-homogeneous Einstein-Kaehler Fano manifold as a base-space, then we can obtain an example of non-almost-homogeneous Kaehler-Ricci soliton.

Academic Significance and Societal Importance of the Research Achievements

Einstein・Kaehler計量やその一般化である定スカラー曲率Kaehler計量,端的Kaehler計量,Kaehler・Ricciソリトン等の知られている具体例は,大きな群が作用する概等質的なものがほとんどである.我々の考えたKSM多様体は底空間として勝手なEinstein・Kaehler・Fano多様体を考えることができるので,等質的でないEinstein・Kaehler・Fano多様体を底空間に選べば,概等質的でないKaehler・Ricciソリトンを多数構成できる.

Report

(7 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (15 results)

All 2020 2019 2018 2017 2016 2015

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (10 results) (of which Int'l Joint Research: 1 results,  Invited: 10 results)

  • [Journal Article] Kaehler-Ricci solitons on certain toric bundles2019

    • Author(s)
      Yasuhiro Nakagawa
    • Journal Title

      Kyusyu Journal of Mathematics

      Volume: 73

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Periodic surfaces of revolution in R^3 and closed plane curves2019

    • Author(s)
      Yasuhiro Nakagawa and Hidekazu Sato
    • Journal Title

      Recent topics in differential geometry and its related fields

      Volume: 会議録

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Kaehler-Ricci solitons on certain toric bundles2019

    • Author(s)
      Yasuhiro Nakagawa
    • Journal Title

      Kyushu Journal of Mathematics に掲載予定

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Periodic surfaces of revolution in R^3 and closed plane curves2019

    • Author(s)
      Yasuhiro Nakagawa and Hidekazu Sato
    • Journal Title

      Recent Topics in Differential Geometry and its Related Fields に掲載予定

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the examples of Nill and Paffenholz2015

    • Author(s)
      Yasuhiro Nakagawa
    • Journal Title

      International Journal of Mathematics

      Volume: 26 Issue: 04 Pages: 673687-673687

    • DOI

      10.1142/s0129167x15400078

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] KSM 多様体上の満渕ソリトンについて2020

    • Author(s)
      中川 泰宏
    • Organizer
      淡路島幾何学研究集会 2020
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] KSM 多様体上の Kaehler・Ricci ソリトン2019

    • Author(s)
      中川 泰宏
    • Organizer
      淡路島幾何学研究集会 2019
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 周期的な回転面と平面閉曲線について(招待講演)2018

    • Author(s)
      中川 泰宏
    • Organizer
      淡路島幾何学研究集会 2018
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] ある種のトーリック束の上の Kaehler・Ricci ソリトンについて2017

    • Author(s)
      中川 泰宏
    • Organizer
      淡路島幾何学研究集会 2017
    • Place of Presentation
      淡路島 国民宿舎 慶野松原荘
    • Year and Date
      2017-01-27
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] ある種のトーリック束の上の Kaehler・Ricci ソリトンの存在問題について2016

    • 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
      2016-11-03
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] On the exsitence problems for Kaehler-Ricci solitons on certain toric bundles2016

    • Author(s)
      中川 泰宏
    • Organizer
      第 22 回複素幾何シンポジウム(金沢) (The 22nd Symposium on Complex Geometry)
    • Place of Presentation
      金沢県政記念 しいのき迎賓館
    • Year and Date
      2016-11-01
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] ある種のトーリック束の上の Einstein・Kaehler 計量の存在問題について2016

    • Author(s)
      中川 泰宏
    • Organizer
      2016 名城幾何学研究集会「幾何構造の深化」
    • Place of Presentation
      名城大学理工学部
    • Year and Date
      2016-03-01
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] ある種のトーリック束の上の Einstein-Kaehler 計量について2016

    • Author(s)
      中川 泰宏
    • Organizer
      淡路島幾何学研究集会 2016
    • Place of Presentation
      淡路島国民宿舎 慶野松原荘
    • Year and Date
      2016-01-22
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] ある種のトーリック束の上の Kaehler・Ricci ソリトンの存在問題2016

    • Author(s)
      中川 泰宏
    • Organizer
      東工大幾何セミナー
    • Place of Presentation
      東京工業大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 非対称 Einstein・Kaehler トーリック Fano 多様体について2015

    • Author(s)
      中川 泰宏
    • Organizer
      RIMS 研究集会「幾何学・組合せ論に現れる環と代数構造」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-06-09
    • Related Report
      2015 Research-status Report
    • Invited

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Published: 2015-04-16   Modified: 2022-01-27  

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