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A STUDY ON GEOMETRICALLY ANALYTIC STRUCTURES ON COMPLEX BOUNDED DOMAINS

Research Project

Project/Area Number 10440040
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTOYAMA UNIVERSITY

Principal Investigator

AZUKAWA Kazuo  TOYAMA UNIVERSITY, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (20018998)

Co-Investigator(Kenkyū-buntansha) NOGUCHI Jyunjirou  UNIVERSITY OF TOKYO, DEPARTMENT OF MATHEMATICS, PROFESSOR, 大学院・数理科学研究所, 教授 (20033920)
KODA Takashi  TOYAMA UNIVERSITY, FACULTY OF SCIENCE, ASSISTANT PROFESSOR, 理学部, 助教授 (40215273)
WATANABE Yoshiyuki  TOYAMA UNIVERSITY, FACULTY OF SCIENCE, PROFESSOR, 理学部, 助教授 (50018991)
SHIMIZU Satoru  TOHOKU UNIVERSITY, DEPARTMENT OF MATHEMATICS ASSISTANT PROFESSOR, 大学院・理学研究科, 助教授 (90178971)
KODAMA Akio  KANAZAWA UNIVERSITY, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (20111320)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥7,000,000 (Direct Cost: ¥7,000,000)
Fiscal Year 2000: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1999: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1998: ¥3,100,000 (Direct Cost: ¥3,100,000)
KeywordsPluri complex Green function / Bergman metric / Homogeneous bounded domain / Leap year / Latai square / Magic square / plane tiling / 等質有界領域 / 不変計量 / 擬対称領域 / 正則双断面曲率 / 連分数展開
Research Abstract

The original purpose of this research is, firstly, that for every covering mapping between complex manifolds, when the fundamental inequality on pluri-complex Greeen functions of these manifolds become to an equality? To investigate this, we wanted to examine some examples. Secondly, we wanted to answer to the question if the holomorphic bisectional curvature of the Bergman metric on homogeneous bounded domain in the euclidian space are non-positive, then is the domain guasi symmetric in the sense of Satake. Unfortunately, we could not get good answers to these problems. However, we get the following three related results :
(1)Cosidering upper forward extending continued fraction expansion of a real number, we proved that if we take a leap year once 4 years, skip the last doing once 32 years, and skip the last doing once 691 years, and skip the last doing once 703, then the difference between the true time, the mean solar time, and the calender time is at most 24 hours.
(2)For A and B mutually prime, let p be the sum of the square of A and of B.Assume that p is odd. Then, (i)there exists two orthogonal Latin squares, which are antipodally complete, and(ii)there exists an antipodally complete magic square of order p.
(3)For every integer N at least 5, there estists a plane tiling by a parallel hexagon such that the congruent transformation group is a rotation goup of order N.

Report

(4 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (38 results)

All Other

All Publications (38 results)

  • [Publications] Suzuki, M.: "On the bifurcations of plane quadratic maps"Math.J.Toyama Univ.. 23. 115-126 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Abe, Y.: "Universal functions on complex special linear groups"Proc.Fourth International Conf.Difference Eq., Poeran,1998. 1-8 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Noguchi,J.: "The value distribution of holomorphic curves into semi-Abelian varieties"C.R.Acad.Sci.Paris. 331. 235-240 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kodama, A.: "A remark on generalized complex ellipsoids with spherical boundary points"J.Korean Math.Soc. 37. 285-295 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Shimizu, S.: "A classification of two-dimensional tube domains"Amer.J.Math.. 122. 1289-1308 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Suzuki: "On the bifurcations of plane quadratic maps"Math.J.Toyama Univ.. 23. 115-126 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Abe: "Universal functions on complex general linear groups"J.Approximation Theory. 100. 221-232 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Abe: "Meromorphic functions admitting an algebraic addition theorem"Osaka J.Math.. 36. 343-363 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Abe: "Universal functions on complex special linear groups"Proceedings of the Fourth International Conference on Difference Equations, Poznan. 1998. 1-8 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Watanabe: "Quaternion K" aher structures on the tangent bundle of a complex spaceform"Rendi.Istit.Mat.Univ.Trieste. 30. 351-370 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Watanabe: "New structures on tangent bundles"Note di Matemamatica(Lecce). 18. 131-141 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Watanabe: "From Sasakian 3-structures to quaternionic geometry"Arch.Math.(BRNO). 34. 379-386 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Koda: "Weakly symmetric nearly K" ahler manifolds"Bull.Math.Soc.Sci.Math.Roumanie. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] J.Noguchi: "On holomorphic curves in semi-Abelian varieties"Math.Z.. 228. 713-721 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] J.Noguchi: "Value distribution theory of holomorphic mappings"Cotemp.Math.. 222. 109-129 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] J.Noguchi: "The value distribution of holomorphic curves into semi-Abelian varieties"C.R.Acad.Sci.Paris. 331. 235-240 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] J.Noguchi: "Holomorphic curves and integral points of divisors"preprint UTMS 99-6, math. 9902014. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] J.Noguchi: "The second main theorem for holomorphic curves into semi-Abelian varieties"preprint UTMS 99-49, math. 9912086. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] A.Kodama: "A characterization of certain weakly pseudoconvex domains"Tohoku Math.J.. 51. 55-64 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] A.kodama: "A remark on generalized complex ellipsoids with spherical boundary points"J.Korean Math.Soc.. 37. 285-295 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Shimizu: "Automorphisms and equivalence of tube domains with bounded base"math.Ann.. 315. 295-320 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Shimizu: "A classification of two-dimensional tube domains"Amer.J.Math.. 122. 1289-1308 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Suzuki,M.: "On the bifurcations of plane quadratic maps"Math,J.Toyama Univ.. 23. 115-126 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Abe,Y.: "Universal functions on complex specialliness groups"Proceedings of the Fourth Int.Conf.on Dif.Eg.,Poznan,1998. 1-8 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Noguchi,J.: "The value distribution of hdomoyhic curves into semi-Abelian"C.R.Acad.Sci.Paris. 331. 235-240 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kodama,A.: "A remark on generalized complex ellipsoids with spherical boundary points"J.Korean Math Soc.. 37. 285-295 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Shimizu,S.: "A classification of two-dimensioral tubo domains"Amer.J.Math.. 122. 1289-1308 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Watanabe Y.: "Quaternion Kahler structures on the tangent bundle of a complex form"Rendi. Ist. Mat. Univ. Trieste.

    • Related Report
      1999 Annual Research Report
  • [Publications] Watanabe Y.: "New structures on tangent bundles"Note di Matematica (Lecce).

    • Related Report
      1999 Annual Research Report
  • [Publications] Abe Y.: "Universal functions on complex general linear groups"J. Approximation Theory. 100. 221-232 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Abe Y.: "Meromorphic functions admitting an algebraic addition theorem"Osaka J. Math.. 36. 343-363 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Noguchi J.: "Value distribution theory of holomorphic mappings"Contemp. Math.. 222. 109-129 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kodama A.: "A characterization of certain weakly pseudoconvex domains"Tohoku Math. J.. 51. 55-64 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Watanabe, Y.: "From Sasakian3-structures to quaternionic geometry" Arch. Math. (BRNO). 379-386 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Noguchi, J.: "On holomorphic curves insemi-Abelian varieties" Math.Z.228. 713-721 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Noguchi, J.: "Value distribution theory of holomorphic mappings" Contemp. Math.222. 109-129 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Kodama, A.: "A characterization of certain weakly pseudoconvex domains" Tohoku Math. J.51. 55-64 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Shimizu, S.: "Automorphisms and equivalence of tube domains with bounded base" Math. Ann.

    • Related Report
      1998 Annual Research Report

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

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