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

Study on global structures of manifolds.

Research Project

Project/Area Number 03640048
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

IMANISHI Hideki  Kyoto Univ.,Integrated Human Studies,Professor, 総合人間学部, 教授 (90025411)

Co-Investigator(Kenkyū-buntansha) GYOJO Akihiko  Kyoto Univ.,Integrated Human Studies,Assistant Professor, 助教授 (50116026)
HATA Masayoshi  Kyoto Univ.,Integrated Human Studies,Assistant Professor, 助教授 (40156336)
FUJIKI Akira  Kyoto Univ.,Graduate School of Human&Environment Studies,Assist.Professor, 教授 (80027383)
TANDAI Kouichi  Kyoto Univ.,Integrated Human Studies,Professor, 総合人間学部, 教授 (90026732)
TAKEUCHI Akira  Kyoto Univ.,Integrated Human Studies,Professor, 総合人間学部, 教授 (40026761)
Project Period (FY) 1991 – 1992
Project Status Completed (Fiscal Year 1992)
Budget Amount *help
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1992: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1991: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsGrassmann manifold / invriant differential operator / Kahler manifold / Einstein-Kahler metric / Dolbeault lemma / Diophantine approximation / ケ-ラ-多様体 / ハイバ-ケ-ラ-空間 / モジュライ / ラドン変換
Research Abstract

Here we summarize some of our published results listed below. [1],[2]: Let M be the Grassmann manifold of real or complex two planes respectively. A set of generators of the ring of invariant differential operators on M is determined and the eigenspace decompositions are obtained. [3]: A necessary and sufficient condition for the existence of an extremal Kahler metric on some ruled manifolds is obtained and some interesting relations between the problems of existence and uniqueness of the metric are observed. [4]: The L^2-Dolbeault lemma is established for holomorphic Hermitian vector bundles on pseudo projective manifolds. The lemma is applied to the problems of deformation of locally bounded symmetric domains and to the problem of existence of Kahler-Einstein metrics. [5],[6]: Here the problem of rational approximations of some irrational numbers are considered. This research is based on highly acculate numerical experiences which is developed through the authors research on dynamical systems.

Report

(3 results)
  • 1992 Annual Research Report   Final Research Report Summary
  • 1991 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] K.TANDAI(with T.Sumitomo): "Invariant differential operators on the Grassmann manifold SG_<2.n-1>(R)." Osaka Journal of Mathematics. 28. 1017-1033 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] K.TANDAI(with T.Sumitomo): "Invariant differential operators on the Grassmann manifold SG_<2.n-1>(C)." Osaka Joural of Mathematics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Akira FUJIKI: "Remarks on extremal Kahler metrics on ruled manifolds." Nagoya Math Journal. 126. 89-102 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Akira FUJIKI: "An L_2-Dolbeault lemma and its applications." Publ RIMS,Kyoto Univ.29.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Masayoshi HATA: "A lower bound for rational approximations to π." Journal of Number Theory.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Masayoshi HATA: "Rational approximations to the dilogarithm." Transaction A men.Math.Soc.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Tandai,K.(with Sumitomo,T.): "Invariant differntial operators on the Grassmann manifold SG2,n-l(R)" Osaka Journal of Math.vol.28. 1017-1033 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Tandai,K.(with Sumitomo,T.): "Invariant differential operators on the Grassmann manifold SG2,n-l(C)" Osaka Journal of Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Fujiki,Akira: "Remarks of extremal Kahler metrics of ruled manifolds." Nagoya Math.Journal. vol.126. 89-102 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Fujiki,Akira.: "An L2-Dolbeault lemma and its applications." Publ.RIMS,Kyoto Univ.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Hata,Masayoshi: "A lower bound for rational approximations to pi." Journal of Number Theory.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Hata,Masayoshi: "Rational approximations to the dilogarithm." Transaction Amer.Math.Soc.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] K.Tandai (with T.Sumitomo): "Invariant differential operators on the Grassmann manifold SG_<2,n-1>(R)." Osaka J. of Mathematics. 28. (1991)

    • Related Report
      1992 Annual Research Report
  • [Publications] K.Tandai (with T.Sumitomo): "Invariant differential operators on the Grassmann manifold SG_<2,n-1>(C)." Osaka J. of Mathematics.

    • Related Report
      1992 Annual Research Report
  • [Publications] Akira FUJIKI: "Remarks on extremal Kahler metrics on ruled manifolds." Nagoya Math.Journal. 126. 89-102 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Akira FUJIKI: "An L^2-Dolbeault lemma and its applications." Publ.RIMS,Kyoto Univ.

    • Related Report
      1992 Annual Research Report
  • [Publications] Masayoshi HATA: "A lower bound for rational approximations to π." Journal of Number Theory.

    • Related Report
      1992 Annual Research Report
  • [Publications] Masayoshi HATA: "Rational approximations to the dilogarithm." Trans.Amer.Math.Soc.

    • Related Report
      1992 Annual Research Report
  • [Publications] 藤木 明: "Hyperkahler structures on the moduli space of blat bandles" Lecture Notes in Mathematics. 1468. 1-83 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 藤木 明: "Romorks on extremal Hahler motrics on rulel manyolds"

    • Related Report
      1991 Annual Research Report
  • [Publications] 藤木 明: "An L^2ーDolbeault lomma andits applications"

    • Related Report
      1991 Annual Research Report
  • [Publications] 旦代 晃一: "Invariant differential operators on the Grassmann manifold S G_2,nー1( )"

    • Related Report
      1991 Annual Research Report
  • [Publications] 旦代 晃一: "Invariant differential operators on the Grassmann manifold S G_2,nー1(C)"

    • Related Report
      1991 Annual Research Report

URL: 

Published: 1991-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi