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

Cross-Subject Study of Geometry

Research Project

Project/Area Number 07640108
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KOBAYASHI Ryoichi  Nagoya University, Graduate School of Polymathematics Professor, 大学院・多元数理科学研究科, 教授 (20162034)

Co-Investigator(Kenkyū-buntansha) YOSHIKAWA Ken-ichi  Graduate School of Polymathematics, Research Associate, 大学院・多元数理科学研究科, 助手 (20242810)
SATO Takeshi  Graduate School of Polymathematics, Research Associate, 大学院・多元数理科学研究科, 助手 (60252219)
MUKAI Shigeru  Graduate School of Polymathematics, Professor, 大学院・多元数理科学研究科, 教授 (80115641)
SATO Hajime  Graduate School of Polymathematics, Professor, 大学院・多元数理科学研究科, 教授 (30011612)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1996: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1995: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsNevanlinna theory / Diophuntine approximation / Weil funition / Riiu-flat Kahlir metrus / Monge-Ampere equation / weightel isoperimetric inequalty / Blaschke conjecture / adapted complex structure / Blaschke多様体 / Monge-Ampere方程式 / 正則曲線 / Diophantine approximation / 分岐個数関数 / 対数微分の補題 / Rothの定理 / 接近関数 / ジェット微分
Research Abstract

The purpose of this project is to study problems in geometry in which several different areas are involved. As a first example, we investigated the possibility of establishing the so far unknown "geometry" which unifies Nevanlinna theory and Diophantine approximations. The main difficulty is the lack of the notion of differentiation of rational points of arithmetically defined projective varieties. We obtained functional equations among Weil functions of jets of holomorphic curves which is expected to serve as "defining equations" of differentials of rational points in Spec Z direction.
Secondly we investigated problems concerning the existence of Ricci-flat Kahler structures on the tangent bundle of compact symmetric spaces. For instance, to show the existence of a Ricci-flat Kahler structure on tangent bundles of compact symmetric spaces of rank at least 2, we must show a priori estimates for solutions of certain Monge-Ampere eqations under appropriate boundary conditions. We overcome this analytic problem by introducing weighted isoperimetric inequality. An interesting question in rank 1 case is to characterize such spaces. The Blaschke conjecture asks to recover the symmetry hidden behind the periodic behavior of geodesics. We showed the existence of a unique complete non-compact Ricci-flat Kahler structure on the complexified Blaschke manifold. By using this, we showed that symmetry (which is shown to exist) at infinity propagates to symmetry of the original Blaschke manifold.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Ryoichi Kobayashi: "Geomelric measure theory and manifoldr of nonnegative Ricci curvature" Proc. Japan acad. 72A. 126-128 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayashi: "Holomorphic Curves in Abelianvariety-the sewnd main thevrem" Nagoya math. J.(発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayashi: "Restructuring value distribution thebry" Gesmetrin Complex Analysis " (World Scientific). 337-354 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayashi: "Ricci-flat Kahlbr metria on symmetric varieties" Comm. geometry and analysis. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 小林亮一: "Nevanlinna理論と数論" 数学(岩波書店). 48-2. 113-127 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayashi: "Valve distribution of holomorphic wrves in projetive algebraio vauri and gelmetru diophantine problems" Compbx gwmetry and sim grlarities. (Interssat press). (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayashi: "Nevanlina Theory and Number Theory (in Japanese)" Sugaku. 48-2. 113-127 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayashi: "Restructuring value distribution theory" Geometric Complex Analysis, World Scientific. 337-354 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayashi: "Value distribution of holomorphic curves into projective algebraic varieties and geometric diophantine problems" Complex Geometry and Singularities. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Yoe Itokawa and Ryoichi Kobayashi: "Geometric measure theory and manifolds of nonnegative Ricci curvature." Proc.Japan Acad.72-A. 126-128 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayashi: "Holomorphic curves in Abelian varieties-second main theorem and application" Nagoya Math.J..(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Hassan Azad and Ryoichi Kobayashi: "Ricci-flat Kahler metrics an symmetric varieties" Comm.Geometry and Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ryoichi Kobayoshi: "Geometric measure theory and manifolds of nonnegative Ricci curvature" Proc.Japan acad.72A. 126-128 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Ryoichi Kobayashi: "Holomorphic curves in Abelian varieties - the second main theorem" Nagoya Math.J.(発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] Ryoichi Kobayashi: "Restructuring value distribution theory" “Geometric Complex Analysis" (World Scientific). 337-354 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] Ryoichi Kobayashi: "Ricci-flat Kahler metrics on symmetric varieties" Comm.geometry and analysis. (発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] Ryoichi Kobayashi: "Value distribution of holomorphic curves into projective algebraic varieties and geometric diophantine problems" “Complex Geometry and Singularities" (Internat.Press.). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 小林亮一: "Nevanlinna理論と数論" 数学(岩波書店). 48-2. 113-127 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 小林亮一: "Value distribution theor of holomorphic curves into complex projective algebraic varieties and geometric Diophantine problems." International Seminar of Singularities and Complex Geometry (International Press). (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 小林亮一: "Restructuring value distribution theory" Geometric Complex Analysis (World Scientific). (to appear). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 小林亮一: "Nevanlinna理論と数論(論説)" 数学(岩波書店). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 小林亮一: "Homorphic curves in Abelian varieties;the second main theorem and application" Nagoya Math.J.(to appear). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 小林亮一(H.Azadと共著): "Ricci-flat Kahler metrics on symmetric varieties" Communications in geometry and analysis. (to appear). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 小林亮一(Y.Itokawaと共著): "Geometric measure theory and manifolds of nonnegative Ricci curvature" Proc.Japan Academy. (to appear). (1996)

    • Related Report
      1995 Annual Research Report

URL: 

Published: 1995-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi