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2013 Fiscal Year Final Research Report

Study of hypergeometric functions

Research Project

  • PDF
Project/Area Number 23540214
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKyushu University

Principal Investigator

YOSHIDA Masaaki  九州大学, 数理(科)学研究科(研究院), その他 (30030787)

Project Period (FY) 2011 – 2013
Keywords超幾何関数 / 黒写像
Research Abstract

1) Original Schwarz map has the Riemann sphere as its target. I proposed the hyperbolic and de Sitter Schwarz maps, whose targets are hyperbolic 3-space and de Sitter 3-space, respectively. The unit normals of the hyperbolic Schwarz image surface are de Sitter Schwarz maps, and vice versa. Geodesic extension of the normals hit the ideal boundary which turn out to be the original and the derived Schwarz maps. These new maps have singularities outside the singularities of the differential equation. These singularities offer geometric invariants.
2) Hyperplane arrangements in the real projective spaces. n+3 hyperplanes in general position in n-space is combinatorially unique. I studied the action of the cyclic group of order n+3 on the chambers cut out by these hyperplanes.

  • Research Products

    (11 results)

All 2014 2013 2012

All Journal Article (4 results) Presentation (7 results)

  • [Journal Article] Monodromy of Lauricella's hypergeometric $F_A$-system2014

    • Author(s)
      K. Matsumoto
    • Journal Title

      Ann. Sc. Norm. Super. Pisa XIII

      Pages: 1-27

  • [Journal Article] Six points/planes in the 3-space2012

    • Author(s)
      K. Cho and K. Yada
    • Journal Title

      Kumamoto J. Math

      Volume: 25 Pages: 17-52

  • [Journal Article] Veronese arrangements of hyperplanes in real projective spaces2012

    • Author(s)
      K. Cho
    • Journal Title

      Internat J Math

      Volume: 23 Pages: 1-16

  • [Journal Article] Discrete flat surfaces and linear Weingarten surfaces in hyperbolic 3-space2012

    • Author(s)
      T. Hoffmann, W. Rossmann, T. Sasaki
    • Journal Title

      Transactions of AMS

      Volume: 364 Pages: 5605-5644

  • [Presentation] Schwarz maps for hypergeometric functions2014

    • Place of Presentation
      Nijmegen (Holland)
    • Year and Date
      20140100
  • [Presentation] Schwarz maps for hypergeometric functions2013

    • Place of Presentation
      Mulhouse (France)
    • Year and Date
      20131100
  • [Presentation] Schwarz maps for hypergeometric functions2013

    • Place of Presentation
      Istanbul (Turkey)
    • Year and Date
      20130600
  • [Presentation] 超幾何的黒写像, 部分多様体の幾何2013

    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      20130600
  • [Presentation] 無手勝流で臨む超幾何微分方程式の可約性2013

    • Organizer
      超幾何研究集会
    • Place of Presentation
      神戸大学
    • Year and Date
      20130100
  • [Presentation] 超幾何的黒写像2013

    • Organizer
      超幾何研究集会
    • Place of Presentation
      神戸大学
    • Year and Date
      20130100
  • [Presentation] 射影空間内の6枚の平面によって切り出される多面体2012

    • Organizer
      超幾何研究集会
    • Place of Presentation
      神戸大学
    • Year and Date
      20120100

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Published: 2015-07-16  

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