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2000 Fiscal Year Final Research Report Summary

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
KeywordsPluri complex Green function / Bergman metric / Homogeneous bounded domain / Leap year / Latai square / Magic square / plane tiling
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.

  • Research Products

    (22 results)

All Other

All Publications (22 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 2002-03-26  

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