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Compact complex homogeneous manifolds with non-degenerate closed 2-forms

Research Project

Project/Area Number 16K05131
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Yamada Takumi  島根大学, 学術研究院理工学系, 准教授 (40403117)

Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords等質空間 / リー群 / リー環 / 複素構造 / ホッジ数 / 擬ケーラー構造 / 正則シンプレクティック構造 / ベキ零多様体 / ドルボーコホモロジー群 / べき零多様体 / 不変複素構造 / リー環のコホモロジー / 正則ベクトル場のなすリー環 / 幾何学
Outline of Final Research Achievements

I studied compact complex homogenous manifolds by using non-degenerate closed 2-forms. In particular, I had results on relations between invariant complex structures and Hodge numbers on compact nilmanifolds. I also had a homeomorphism between the Lie algebra of the holomorphic vector fields and a Dolbeault cohomology group on a compact complex nilmanifold. As an application,I had a necessary condition for admitting pseudo-koehler metric on a compact complex nilmanifold.

Academic Significance and Societal Importance of the Research Achievements

ケーラー等質多様体に関しては多くの研究があり、複素幾何的構造もよくわかっている。一方、非ケーラー等質多様体についてはあまりわかっていない。本研究成果の意義は、非ケーラーである複素ベキ零多様体において、ホッジ数や正則ベクトル場のなすリー環、擬ケーラー構造のはいるための必要条件などの複素幾何的構造がわかったことである。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (10 results)

All 2018 2017 2016

All Journal Article (6 results) (of which Peer Reviewed: 6 results,  Open Access: 5 results,  Acknowledgement Compliant: 4 results) Presentation (4 results) (of which Invited: 3 results)

  • [Journal Article] Complex structures on the complexification of a real Lie algebra2018

    • Author(s)
      Yamada Takumi
    • Journal Title

      Complex Manifolds

      Volume: 5 Issue: 1 Pages: 150-157

    • DOI

      10.1515/coma-2018-0010

    • NAID

      40022258178

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds2017

    • Author(s)
      Takumi Yamada
    • Journal Title

      Complex Manifolds

      Volume: 4 Issue: 1 Pages: 73-83

    • DOI

      10.1515/coma-2017-0006

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Complex structures and non-degenerate closed 2-forms of compact real parallelizable nilmanifolds2017

    • Author(s)
      Takumi Yamada
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 54 Pages: 121-128

    • NAID

      120006240155

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A construction of lattices in splittable solvable Lie groups2016

    • Author(s)
      Takumi Yamada
    • Journal Title

      Kodai Mathematical Journal

      Volume: 39 Pages: 378-388

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Hodge numbers and invariant complex structures of compact nilmanifolds2016

    • Author(s)
      Takumi Yamada
    • Journal Title

      Complex Manifolds

      Volume: 3 Issue: 1 Pages: 193-206

    • DOI

      10.1515/coma-2016-0007

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Remarks on Hodge numbers and invariant complex structures of compact nilmanifolds2016

    • Author(s)
      Takumi Yamada
    • Journal Title

      Complex Manifolds

      Volume: 3 Issue: 1 Pages: 271-281

    • DOI

      10.1515/coma-2016-0014

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] Complex structures on complexification of a real Lie algebras2018

    • Author(s)
      Takumi Yamada
    • Organizer
      RIMS共同研究(公開型) 部分多様体の幾何学の深化と展開
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Invariant complex structures on compact nilmanifolds2017

    • Author(s)
      Takumi Yamada
    • Organizer
      Workshop on Geometry in Oita
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Invariant complex structures and Hodge numbers of compact nilmanifolds2016

    • Author(s)
      山田 拓身
    • Organizer
      広島微分幾何学研究会
    • Place of Presentation
      広島大学
    • Year and Date
      2016-10-06
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Remarks on Hodge numbers and invariant complex structures of compact nilmanifolds2016

    • Author(s)
      山田 拓身
    • Organizer
      RIMS研究集会 部分多様体の微分幾何学的研究
    • Place of Presentation
      京都大学 数理解析研究所
    • Year and Date
      2016-06-27
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2020-03-30  

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