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Projective structures on compex manifolds

Research Project

Project/Area Number 09640129
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionSophia University

Principal Investigator

KATO Masahide  Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (90062679)

Co-Investigator(Kenkyū-buntansha) TAHARA Hidetoshi  Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (60101028)
KANEYUKI Soji  Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (40022553)
NAGANO Tadashi  Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (10189144)
YOKOYAMA Kazuo  Sophia University, Department of Mathematics, Asso. Professor, 理工学部, 助教授 (10053711)
MIYAOKA Reiko  Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (70108182)
谷口 肇  上智大学, 理工学部, 助教授 (40053657)
並河 良典  上智大学, 理工学部, 助教授 (80228080)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1997: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywordscomplex manifold / projective structure / Gauduchon metric / Hartogs domain / non-Kahler / extension peoblem / Weyl curvature teusor / Chern forms / Characteristic forms / projective connections / 正則写像 / Gauduchonメトリック / 特異ファイバー / 正則拡張性
Research Abstract

Our main object of study is a class of compact complex 3-manifolds which contain a subdomain U biholomorphic to a neighborhood of a projective line ill a complex projective 3-space. We call such a class of manifolds by Class L. Such manifolds do not admit projective structures in general, but very deeply related to complex manifolds which admit projective structures. To classify all Class L. manifolds, it seems very important to consider the existence problem of Cauduchon metric near a singular fibre of a 1-parameter family of surfaces, and we are now very near to the complete solution.
To carry out our plan of classification of Class L manifolds, a series of theorems of S. Ivashkovich on the extension of meromorphic maps play important roles. On the other hand, our manifolds of Class L supply us with many interesting examples on extension problems of meromorphic maps. N. Okada (Sophia Univ. Graduate Course) constructed an example of Schottky type Class L manifolds, gave a holomorphic map of a Hartogs domain to the manifold whichl cannot he extended meromorphically across a fractal set, and estimated the Hausdorff dimension of the singular set. With Y. Kamozawa (NTT), we have obtained a explicit formula of characteristic forms on a holomorphic foliation which admits a holomorphic projective connection.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] Y. Komazawa: "On characteristic forms of holomorphic foliations"Tokyo J . Math.. 22. 43-64 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 加藤昌英: "Compact quotient manifolds of domains in a compact complex-dimensional projective space and the Lebesgue measure of limit sets."北海道大学数学講究録. 55. 28-29 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kamozawa, Yoshikatsu; Kato, Masahide: "On characteristic forms of holomorphic foliations"Tpkyo J. Math.. 22. 43-64 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kato, Masahide: "Compact quotient manifolds of domains in a compact complex 3-dimensional projective space and the Lebesgue measure of limit sets"Hokkaido Univ. Sugaku Kokyu-roku. 55. 28-29 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y.Komozawa: "On characteristic forms of holemorphic foliations"Tokyo J.Math.. 22. 43-64 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Kamozawa : M. Kato: "On characteristic forms of holomorphic foliations" Tokyo Journal of Mathematics. 22-1. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] H. Tahara: "On the unigueness theovem for non linear singular partial differential eguations" Journal of Math. Scie Univ Tokyo. 5. 477-506 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] R. G'erard ; H. Tahara: "Formal power senes solutions of nonlivear first order partial differential eguration" Funkeialaj Ekvacioj. 41. 133-160 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ikeda, Yamashita, Yokohama: "Symbolic Description of Homeomorphisms on closed 3-manifolds" Kobe J. Math. 13. 69-115 (1996)

    • Related Report
      1998 Annual Research Report
  • [Publications] 加藤昌英: "Compact quotieut manifolds of domains in a complex 3-dimensional projective space and the Lebesgue measure of liuit Rets" Tokyo J.Math.19. 99-119 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 加藤昌英: "Classifging global strongly pseudocnuex hypevrsurfacos on conydact complex spaces" Kyushu J.Math.49. 123-133 (1995)

    • Related Report
      1997 Annual Research Report
  • [Publications] 加藤昌英: "Logarithmic projective connections" Tokyo J.Math.16. 99-119 (1993)

    • Related Report
      1997 Annual Research Report
  • [Publications] 長野 正: "Symmetric spaces and Quoternionic structures" Proc.of Meeting "Quoternionic Str in Math and Physics. 233-247 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 長野 正: "The involutims of ceupact symnetric spaces III" Tokyo J.Math.18. 193-212 (1995)

    • Related Report
      1997 Annual Research Report
  • [Publications] 並河良典: "Global Rmoothing of Calabi-Yau threefolds" Inveutiones Math.122. 403-419 (1995)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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