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

Research on projective structures Riemaun surfaces from analytic and geometric vieupo

Research Project

Project/Area Number 10640160
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKYUSHU UNIVERSITY (1999)
Nagoya University (1998)

Principal Investigator

TANIGAWA Harumi  Graduate School of Mathematics kyushu university associate professor, 大学院・数理学研究科, 助教授 (30236690)

Co-Investigator(Kenkyū-buntansha) 谷川 晴美  九州大学, 大学院・数理学研究科, 助教授 (30236690)
吉川 謙一  名古屋大学, 大学院・多元数理科学研究科, 助手 (20242810)
内藤 久資  名古屋大学, 大学院・多元数理科学研究科, 助教授 (40211411)
中西 敏浩  名古屋大学, 大学院・多元数理科学研究科, 助教授 (00172354)
江尻 典雄  名古屋大学, 大学院・多元数理科学研究科, 助教授 (80145656)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1998: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsRiemany surfaces / projective structures / Kleinian groups / measured laminations / hyperbolic spaces / 測度つき葉層 / タイヒミュラー空間 / Measured lamination
Research Abstract

In has been known that the space of projective structures on Riemann surfaces has a structure of a vector bundle. This classical fact is based on the fact that a projective structure on a Riemann surface is closely related to a certain differential equation. Therefore, most researches on projective structures have been from analytic viewpoint. However, in mid 80's, Thurston showed that "any projective structure is obtained by grafting some measured lamination to some hyperbolic structure".
The aim of this research has been to investigate projective structures from the above new geometric viewpoint. The classical analytic approach naturally keeps eyes on the underlying complex structure, namely, restrict the observation to each fiber over a complex structure. However, in the course of our research, it turned out that the global observation with the Thurston's geometric parametrization is often more useful than restricting the observation to each fiber, and furthermore, the global observation in turns gives some information about each fiber.
Our approach successfully find out new results, which are interacting each other, can be summed up to the following three points: 1) we showed that on any complex structure, there exist infinitely many exotic structures with fuchsian monodromies and a certain characterization of such structures, 2) in relation to (1), we gave some observation how projective structures with discrete monodromies distribute on each fibers, 3) we proved that for each fiber, the mapping sending each projective structure to its monodromv is proper whenever restricted to anv fiber.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] Harumi Tanigawa: "Grafting, Harmaric Mapsaml Projective structures on surfaces"Journal of Diffierential Geometry. 47. 339-419 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Harumi Tanigawa & Hiroshige Shya: "Projective structures with discrete holonmy representations"Transactions of the American Mathematical Society. 352. 813-823 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Harumi Tanigawa: "Divergence of Projective structures and lengths of measured laminations"Duke Mathematical Journal. 98. 209-215 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Harumi Tanigawa: "Grafting, Harmonic Mansard Projective Structures on surfaces"Joushal of Differential Geolnetry. 47. 399-419 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Harumi Tanigawa: "Projective Structures with dissociate horology repro sensations"Transaction of the American Matthew. 351. 813-823 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Harumi Tanigawa: "Divergence of projective Structures and longish of weasued lamination"Duke Mathematical Jownel. 98. 209-215 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Harumi Tanigawa: "Grafting,Harmonic Maps and Projective structures on surfaces"Journal of Differential Geometry. 47. 399-419 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] Harumi Tanigawa & Hiroshige Shiga: "Projective structures with disorete holonomy representations"Transactions of the American Mathematical Society. 351. 813-823 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Harumi Tanigawa: "Divergence of Projective structures and lengths of measured laminat*"Duke Mathematical Journal. 98. 209-215 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Shiga & H.Tanigawa: "Projective structures with discrite biolonomy representations" Trans.Amer.Math.Sic.(発行予定)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Tanigawa: "Divergence of projective structures and longthis of measured laminations" Duke Math.J.Vl97. (発行予定)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Ejiri: "The boundary of the space of full hanmonir maps of S^2 into S^<2m>(1) and extra iregularfunctions" Japanese Journal of Math.24. 83-121 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Nakanishi & M.Naataneu: "Weil-Petersson aress of the miduli spaceo of Tori" Results in Math.33. 120-133 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Kozono, Y.Maeda & H.Naito: "A Yang-Mills-Higgs gradient flow on R^3 blowing up at infinity" Proc.Japan Acad Ser A. 74. 71-73 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Yoshikawa: "Smoothing of isolated hypersurface singularities and Quillen metrics" Asian J.Math. 2. 101-120 (1998)

    • Related Report
      1998 Annual Research Report

URL: 

Published: 1998-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi