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Astudy on complex and Kaehler structures on compact homogeneous manifolds

Research Project

Project/Area Number 18540075
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionNiigata University

Principal Investigator

HASEGAWA Keizo  Niigata University, Institute of Humanities , Social Sciences and Education, Associate Professor (00208480)

Co-Investigator(Kenkyū-buntansha) SEKIGAWA Kouei  Niigata University, Institute of Sciences and Thchnology, Professor (60018661)
YOSHIHARA Hisao  Niigata University, Institute of Sciences and Technology, Professor (60114807)
Project Period (FY) 2006 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥690,000 (Direct Cost: ¥600,000、Indirect Cost: ¥90,000)
Fiscal Year 2007: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2006: ¥300,000 (Direct Cost: ¥300,000)
Keywordshomogeneous manifolds / complex structures / Kaehler structures / 可解多様体 / 左不変複素構造 / 擬ケーラー構造
Research Abstract

In this research project, we studied one of the problems stated in "Purpose of the Project", and obtained a result "There exists a compact solvmanifold of dimension 6---actually a compact complex solvmanifold of dimension 3---which admit a continuous family of non-left-invariant complex structures as small deformations of the original complex structure". We also determine all three-dimensional compact complex-homogeneous solvmanifolds which admit pseudo-Kaehler structures. The announcement of the result has been published in "Electronic Research Announcements in Mathematical Sciences". We also published a survey article, based on the special lecture given in the annual conference of Mathematical Society of Japan, "Complex and Kaehler structures on compact homogeneous manifolds-their existence, classification and moduli problem".
As another important research activity of the project we held a workshop."Complex Geometry and Group Actions" (Niigata-shi, June 28-30, 2007); and published Proceedings of the workshop, which is available from the homepage: http://math.ed.niigata-u.ac.jp/~admin/workshop.html
We believe that this research project was successful in developing and expanding this area of research, and making it widely known to many researchers in the related fields.

Report

(3 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • Research Products

    (25 results)

All 2008 2007 2006 Other

All Journal Article (20 results) (of which Peer Reviewed: 9 results) Presentation (3 results) Remarks (2 results)

  • [Journal Article] Compact indefinite almost Kaehler Einstein manifolds2008

    • Author(s)
      K. Sekigawa and A. Yamada(関川 浩永, 山田 章)
    • Journal Title

      Geometriae Dedicata Vol.132

      Pages: 65-79

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Compact indefinite almost Kaehler Einstein manifolds2008

    • Author(s)
      K, Sekigawa, A. Yamada
    • Journal Title

      Geometriae Dedicata Vol.132

      Pages: 65-79

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Compact indefinite almost Kaehler Einstein manifolds2008

    • Author(s)
      K. Sekigawa and A. Yamada (関川 浩永, 山田 章)
    • Journal Title

      Geometriae Dedicata Vol.132

      Pages: 65-79

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complex moduli and pseudo-Kaehler structures on three-dimensional compact complex solvmanifolds2007

    • Author(s)
      K. Hasegawa(長谷川 敬三)
    • Journal Title

      Electronic Research Announcements in Mathematical Sciences, Vol.14

      Pages: 30-34

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Galois points for plane rational curves,2007

    • Author(s)
      H. Yoshihara(吉原 久夫)
    • Journal Title

      Far east Journal of Mathematical Sciences Vol.25

      Pages: 273-284

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Complex moduli and pseudo-Kaehler structures on three-dimensional compact complex solvmanifolds2007

    • Author(s)
      K, Hasegawa
    • Journal Title

      Electronic Research Announcements in Mathematical Sciences Vol.14

      Pages: 30-34

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Galois points for plane rational curves2007

    • Author(s)
      H, Yoshihara
    • Journal Title

      Far East Journal of Mathematical Sciences Vol.25

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Complex moduli and pseudo-Kaehler structures on three-dimensional compact complex solvmanifolds2007

    • Author(s)
      K. Hasegawa (長谷川 敬三)
    • Journal Title

      Electronic Research Announcements in Mathematical Sciences Vol.14

      Pages: 30-34

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Galois points for plane rational curves2007

    • Author(s)
      H. Yoshihara (吉原 久夫)
    • Journal Title

      Far East Journal of Mathematical Sciences Vol.25

      Pages: 273-284

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on compact solvmanifolds with Kaehler structures2006

    • Author(s)
      K. Hasegawa(長谷川 敬三)
    • Journal Title

      Osaka Journal of Mathematics Vol.43

      Pages: 131-135

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A note on the integrability of a class of almost quaternionic manifolds,2006

    • Author(s)
      K. Sekigawa and A. Yamada(関川 浩永, 山田 章)
    • Journal Title

      Indian Journal of Mathematics Vol.48

      Pages: 239-248

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Galois lines for space curves,2006

    • Author(s)
      H. Yoshihara(吉原 久夫)
    • Journal Title

      Algebra Colloquium Vol.13

      Pages: 455-469

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A note on compact solvmanifolds with Kaehler Structures2006

    • Author(s)
      K, Hasegawa
    • Journal Title

      Osaka Journal of Mathematics Vol.43

      Pages: 131-135

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A note on the integrability of a class of almost quaternionic manifolds2006

    • Author(s)
      K, Sekigawa, A. Yamada
    • Journal Title

      Indian Journal of Mathematics Vol.48

      Pages: 239-248

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Galois lines for space curves2006

    • Author(s)
      H, Yoshihara
    • Journal Title

      Algebra Colloquium Vol.25

      Pages: 455-469

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A note on compact solvmanifolds with Kaehler structures2006

    • Author(s)
      長谷川 敬三
    • Journal Title

      Osaka Journal of Mathematics 43

      Pages: 131-135

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A note on the integrability of a almost quanterinionic manifolds2006

    • Author(s)
      関川 浩永(共著)
    • Journal Title

      Indian Journal of Mathematics 48

      Pages: 239-248

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Galois lines for space curves2006

    • Author(s)
      吉原 久夫
    • Journal Title

      Algebra Colloquium 13

      Pages: 455-469

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A remark on an example of a 6-dimensional almost Keahler-Einstein manifolds

    • Author(s)
      関川 浩永(共著)
    • Journal Title

      Journal of Geometry (印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Galois points for plane rational curves

    • Author(s)
      吉原 久夫
    • Journal Title

      Far East Journal of Mathematics (印刷中)

    • Related Report
      2006 Annual Research Report
  • [Presentation] Complex and Pseudo-Kaehler structures on compact homogeneous manifolds2007

    • Author(s)
      K. Hasegawa (長谷川 敬三)
    • Organizer
      Niigata Workshop on Complex Geometry and Singularities (新潟研究集会「複素幾何学と特異点」)
    • Place of Presentation
      新潟市クロスパルにいがた
    • Year and Date
      2007-08-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Complex Keahler structures on compact homogeneous manifolds-their existence, classification and moduli problem2007

    • Author(s)
      長谷川 敬三
    • Organizer
      日本数学会年会幾何学分科会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-29
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Complex Keahler structures on compact homogeneous manifolds-their existence, classification and moduli problem2007

    • Author(s)
      K, Hasegawa
    • Organizer
      Special lecture
    • Place of Presentation
      Mathematical Society of Japan
    • Year and Date
      2007-03-29
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Remarks] 「研究成果報告書概要(和文)」より

    • URL

      http://math.ed.niigata-u.ac.jp/~admin/workshop.html

    • Related Report
      2007 Final Research Report Summary
  • [Remarks] 研究会「複素幾何学と群作用」(Workshop on Complex Geometry and Group Actions),2007年6月28日〜30日,新潟市クロスパルにいがた,報告書は次の研究会ホームページにも掲載

    • URL

      http://math.ed.niigata-u.ac.jp/~admin/workshop.html

    • Related Report
      2007 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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