• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study of Complex Structures and Conformal Geometric Structures on Homogeneous Spaces

Research Project

Project/Area Number 25400066
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionNiigata University

Principal Investigator

HASEGAWA KEIZO  新潟大学, 人文社会・教育科学系, 教授 (00208480)

Co-Investigator(Kenkyū-buntansha) KAMISHIMA YOSHINOBU  城西大学, 理学部, 教授 (10125304)
TSUKADA KAZUMI  お茶の水女子大学, 大学院・人間文化創成科学研究科, 教授 (30163760)
MORIYA KATSUHIRO  筑波大学, 数理物理科学研究科, 助教 (50322011)
Co-Investigator(Renkei-kenkyūsha) MABUCHI TOSHIKI  大阪大学, 理学研究科, 名誉教授 (80116102)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords局所共形ケーラー構造 / 等質多様体 / conformal Kaehler / homogeneous complex / ケーラー構造 / 簡約Lie群 / 可解Lie群 / 等質局所共形ケーラー構造 / Vaisman構造 / 国際研究者交流 (ドイツ, ロシア)
Outline of Final Research Achievements

In the field of Complex Geometry "Kaehler structure" is a central subject. As a study of locally conformally Kaehler structures (LCK structure for short) we have shown that a compact homogeneous LCK manifold is a holomorphic fibre bundle over a flag manifold with fiber a 1-complex torus. Furthermore, we have shown that they are all of Vaisman type, that is, its associated Lee form is parallel with respect to the Riemann metric.
As an important research activity during the period of this research project we have organised the international symposium "Complex Geometry and Lie Groups" in Torino, June 16-20, 2015 and in Nara, March 22-26, 2016.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (23 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (2 results) Journal Article (10 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 10 results,  Open Access: 1 results,  Acknowledgement Compliant: 5 results) Presentation (10 results) (of which Int'l Joint Research: 2 results,  Invited: 8 results) Funded Workshop (1 results)

  • [Int'l Joint Research] ハンブルグ大学(ドイツ)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] マサリク大学(チェコ)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Compact Locally conformally Kaehler manifolds2016

    • Author(s)
      K. Hasegawa and Y. Kamishima
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 53

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Totally complex submanifolds of a complex Grassmann manifold of 2-planes2016

    • Author(s)
      K. Tsukada
    • Journal Title

      Differential Geometry and its Applications

      Volume: 44 Pages: 30-51

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Locally conformally Kaehler structures on homogeneous spaces2015

    • Author(s)
      K. Hasegawa and Y. Kamishima
    • Journal Title

      Progress in Mathematics

      Volume: 308 Pages: 353-372

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Homogeneous locally conformally Kaehler and Sasaki manifolds2015

    • Author(s)
      D. Alekseevsky, V. Cortes, K. Hasegawa and Y. Kamishima
    • Journal Title

      International Journal of Mathematics

      Volume: 26 Pages: 1-29

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Surfaces of constant mean curvature with symmetry2015

    • Author(s)
      K. Moriya
    • Journal Title

      Israel Journal of Mathematics

      Volume: 207 Pages: 331-359

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Homogeneous locally conformally Koehler and Sasaki manifolds2015

    • Author(s)
      D. Alekseevsky, V. Cortes, K. Hasegawa and Y. Kamishima
    • Journal Title

      International Journal of Mathematics

      Volume: 印刷中

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] A factorization of a super-conformal map2015

    • Author(s)
      K. Moriya
    • Journal Title

      Israel Journal of Mathematics

      Volume: 印刷中 Issue: 1 Pages: 331-359

    • DOI

      10.1007/s11856-015-1176-6

    • Related Report
      2014 Research-status Report 2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Locally Conformally Kaehler Structures on Homogeneous Spaces2015

    • Author(s)
      K. Hasegawa and Y. Kamishima
    • Journal Title

      Progress in Mathematics

      Volume: 印刷中

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Conformally Flat Lorentz Parabolic Manifolds2014

    • Author(s)
      Y. Kamishima
    • Journal Title

      Central European Journal of Mathematics

      Volume: 12 Pages: 861-878

    • Related Report
      2014 Research-status Report 2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Conformally flat homogeneous Lorentzian manifolds, in Recent Trends in Lorentzian Geometry2013

    • Author(s)
      K. Honda and K. Tsukada
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 26 Pages: 295-314

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Compact locally homogeneous Kaehler and lcK manifolds,2015

    • Author(s)
      長谷川敬三
    • Organizer
      第21回複素幾何学シンポジュウム
    • Place of Presentation
      金沢大学,石川県金沢市
    • Year and Date
      2015-10-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Survey on spherical CR-structures and related geometric structures2015

    • Author(s)
      神島芳宣
    • Organizer
      Workshop on Geometric Structures, Hitchin Components and Representation Varieties
    • Place of Presentation
      KIAS, ソウル(韓国)
    • Year and Date
      2015-10-20
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 極小曲面のシンプル・ファクター・ドレッシング2015

    • Author(s)
      守屋克洋
    • Organizer
      本数学会2015年度年会幾何学分科会一般講演
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Totally complex submanifolds of a complex Grassmann manifold of 2-planes2015

    • Author(s)
      塚田和美
    • Organizer
      微分幾何学ワークショップ「部分多様体の幾何学とリー理論」
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2015-02-12 – 2015-02-14
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Non-Kaehler Geometric Structures on Homogeneous Spaces2015

    • Author(s)
      長谷川敬三
    • Organizer
      Complex Hyperbolic Geometry and Related Topics
    • Place of Presentation
      岡山理科大学
    • Year and Date
      2015-01-09 – 2015-01-11
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On the existence of Vaisman lcK structure on locally homogeneous manifolds2014

    • Author(s)
      神島芳宣
    • Organizer
      Workshop on "Analysis and Geometry in Several Complex Variables"
    • Place of Presentation
      The Institute of Mathematics, Academia Sinica
    • Year and Date
      2014-12-15 – 2014-12-19
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On complex contact similarity manifolds2014

    • Author(s)
      神島芳宣
    • Organizer
      The Kortrijk workshop on Discrete Groups and Geometric Structures
    • Place of Presentation
      Belgium (Leuven)
    • Year and Date
      2014-06-02 – 2014-06-06
    • Related Report
      2014 Research-status Report
  • [Presentation] 四元数射影空間内のウィルモア正則曲線2014

    • Author(s)
      守屋 克洋
    • Organizer
      研究会「多様体上の変分問題とその周辺領域」
    • Place of Presentation
      山口県健康づくりセンター
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On the holomorphic torus Bott tower

    • Author(s)
      神島 芳宣
    • Organizer
      International Conference on Algebraic Topology and Abelian Functions
    • Place of Presentation
      Steklov Institute (Moscow)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 四元数射影空間の複素部分多様体

    • Author(s)
      塚田 和美
    • Organizer
      北海道大学数学教室 幾何学コロキウム
    • Place of Presentation
      北海道大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Funded Workshop] Complex Geometry and Lie Groups (複素幾何学とリー群)2016

    • Place of Presentation
      奈良県奈良市 奈良女子大学
    • Year and Date
      2016-03-22
    • Related Report
      2015 Annual Research Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi