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Visualization of hyperbolic surfaces via generic fundamental polygons, and its applications on the theory of the canonical decomposition

Research Project

Project/Area Number 21740047
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKanazawa University

Principal Investigator

USHIJIMA Akira  Kanazawa University, 数物科学系, 准教授 (50323803)

Project Period (FY) 2009 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords双曲幾何学 / 離散群 / フックス群 / 基本領域 / クライン群
Research Abstract

To visualize hyperbolic surfaces by using of computer, it is required to decide suitable symbolical treatment of such surfaces in this research. I obtained a prototype of such symbolical realization of, not only hyperbolic but also general, surfaces. An advantage of this realization is to detect hyperbolicity of surfaces. Another result is this research is that I obtained a proof of stability of the combinatorial type of generic fundamental polygons of Fuchsian groups when their centers are on the circle at infinity of the hyperbolic plane. This result corresponds to a known result of the same property of generic fundamental polygons with their centers in the hyperbolic plane.

Report

(3 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • Research Products

    (5 results)

All 2011 2009

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

  • [Journal Article] Generic fundament alpolygons for Fuchsian groups2011

    • Author(s)
      Ushijima, A.
    • Journal Title

      Pacific Journal of Mathematics in press

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generic fundamental polygons for Fuchsian groups2011

    • Author(s)
      Akira Ushijima
    • Journal Title

      Pacific Journal of Mathematics

      Volume: (掲載確定)

    • NAID

      120003406328

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] McShane's identities and the volume of M12009

    • Author(s)
      牛島顕
    • Organizer
      Workshop on Weil-Petersson volumes
    • Place of Presentation
      東京工業大学(東京都)
    • Year and Date
      2009-12-21
    • Related Report
      2010 Final Research Report
  • [Presentation] McShane's identities and the volume of M_<1,1>2009

    • Author(s)
      牛島顕
    • Organizer
      Workshop on Weil-Petersson volumes
    • Place of Presentation
      東京工業大学(東京都)
    • Year and Date
      2009-12-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] Symbolic construction of developments of surfaces2009

    • Author(s)
      牛島顕
    • Organizer
      Symbolic description and low-dimensional topology
    • Place of Presentation
      広島大学(広島県)
    • Year and Date
      2009-10-30
    • Related Report
      2010 Final Research Report 2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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