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Topology of Solutions of 1st order PDEs and web g

Research Project

Project/Area Number 14340022
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

NAKAI Isao  Ochanomizu University, Faculty of Science, Professor, 理学部, 教授 (90207704)

Co-Investigator(Kenkyū-buntansha) SUWA Tatsuo  Niigata University, Institute of Science and Technology, Professor, 自然科学系, 教授 (40109418)
SATO Hajime  Nagoya University, Graduate school of Mathmatics, Professor, 大学院・多元数理研究科, 教授 (30011612)
ASUKE Taro  The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (30294515)
TAKEBE Takashi  Ochanomizu University, Faculty of Science, 理学部, 助教授 (60240727)
MAJIMA Hideyuki  Ochanomizu University, Faculty of Science, 理学部, 教授 (50111456)
伊藤 敏和  龍谷大学, 経済学部, 教授 (60110178)
大沢 健夫  名古屋大学, 大学院・多元数理科学研究科, 教授 (30115802)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥11,400,000 (Direct Cost: ¥11,400,000)
Fiscal Year 2005: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2004: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2003: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2002: ¥3,800,000 (Direct Cost: ¥3,800,000)
Keywordscomplex foliation / holomorphic diffeomorphism / web geometry / complex dynamics / ordinary differential equation / ホロノミー / Chern接続 / Campbell-Hausdorff / 関係式 / 複素力学 / Horomorphic diffeomorphism / Relation / 一階微分方程式 / 葉層 / Campbell-Hansdorff / WEB / フェルマー曲面
Research Abstract

We found some nentrivial relations of formal diffeomorphisms of C fixing 0 by the following method. In order to expand words of two formal series in Z∈C, we used the well known Camphell-Hausdorff formula in Lie algebra theory in a generalized form. If all the coefficients are 0, the word in idmtically Z, thus we obtain a relation. The property that the relation holds choosing Taylor coefficients of two diffecs properly is a combinatorial condition on the word.

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (34 results)

All 2005 2004 Other

All Journal Article (22 results) Publications (12 results)

  • [Journal Article] Relations of formal diffeomorphisms2005

    • Author(s)
      中居 功
    • Journal Title

      数理解析研究所講究録 1447

      Pages: 145-163

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] On the geometry of holomorphic flows and foliations having transverse sections.2005

    • Author(s)
      伊藤 敏和
    • Journal Title

      Geometriae Dedicata 111

      Pages: 23-42

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A Poincarae-Hopf-type theorem for holomorphic one-forms2005

    • Author(s)
      伊藤 敏和
    • Journal Title

      Topology 44-1

      Pages: 73-84

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On holomorphic foliations transverse to spheres2005

    • Author(s)
      伊藤 敏和
    • Journal Title

      Moscow Mathematical Journal 2-5

      Pages: 75-93

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] On Quasiconformal Deformations of transversely holomorphic foliations2005

    • Author(s)
      足助 太郎
    • Journal Title

      J.M.S.Japan 57-3

      Pages: 725-734

    • NAID

      130000829431

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On a curvature condition that implies a cohomology injectivity theorem of Kollar-Skoda type2005

    • Author(s)
      大沢 健夫
    • Journal Title

      Publ.RIMS, Kyoto Univ 41

      Pages: 565-577

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Relations of formal diffeomorphisms2005

    • Author(s)
      Isao Nakai, Kana Yanai
    • Journal Title

      RIMS Koukyuroku 1447

      Pages: 145-163

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the geometry of holomorphic flows and foliation having transvers sections2005

    • Author(s)
      Toshikazu Ito
    • Journal Title

      Geometrie Dedicata 111

      Pages: 23-42

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A poincare-Hopf type theorem for holomorphic one forms2005

    • Author(s)
      Toshikazu Ito
    • Journal Title

      Topology 44-1

      Pages: 113-134

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On holomorphic foliations transverse to sphere2005

    • Author(s)
      Toshikazu Ito
    • Journal Title

      Moscow Mathematical Journal 2-5

      Pages: 75-93

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On Quassi conformal Deformation of Transversely holomorphic foliations2005

    • Author(s)
      Taro Asuke
    • Journal Title

      J.M.S.Japan 57-3

      Pages: 725-734

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On a curvature condition that implies a cohomology injectivity theorem of Kollar-Skoda type2005

    • Author(s)
      Takeo Ohsawa
    • Journal Title

      Publ.RIMS.Kyoto Univ. 41

      Pages: 565-577

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the geometry of Holomorphic flows and foliations having transverse sections2005

    • Author(s)
      伊藤 敏和
    • Journal Title

      Geometriae Dedicata 111

      Pages: 23-42

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A Poincare-Hopf-type theorem for holomorphic one forms2005

    • Author(s)
      伊藤 敏和
    • Journal Title

      Topology 44-1

      Pages: 73-84

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On Quasiconformal Deformations of Transversely Holomorphic foliations2005

    • Author(s)
      足助 太郎
    • Journal Title

      J.M.S.Japan 57-3

      Pages: 725-734

    • NAID

      130000829431

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On a curvature condition that implies a cohomology injectivity theorem of Kollar-Skoda type2005

    • Author(s)
      大沢 健夫
    • Journal Title

      Publ.RIMS, Kyoto Univ. 41

      Pages: 565-577

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A Poincare-Hopf-type theorem for holomorphic one-forms2005

    • Author(s)
      T.Ito
    • Journal Title

      Topology 44

      Pages: 73-84

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Residnes for holomorphic foliations of singnlar pairs.2005

    • Author(s)
      T.Suwa
    • Journal Title

      Advances in Geom 5

      Pages: 81-95

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Holomorphic foliations of codimension one transverse to polydiscs2004

    • Author(s)
      T.Ito
    • Journal Title

      Journal for die reine und angewandte Math. 575

      Pages: 37-44

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Residnes for singular pairs and dynamics of biholomorphic maps of singnlar surfaces.2004

    • Author(s)
      T.Suwa
    • Journal Title

      Intern.J.Math 15

      Pages: 443-466

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On Holomorphic foliations Transverse to sphere

    • Author(s)
      T.Ito
    • Journal Title

      Moscow Mathematical Journal (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the geometry of holomorphic flows and foliations having transverse sections

    • Author(s)
      T.Ito
    • Journal Title

      Geometry Dedicata (発表予定)

    • Related Report
      2004 Annual Research Report
  • [Publications] T.Ohsawa: "On the extension of L^2 holomorphic functions VI"Contemp.Math. 332. 235-239 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Ohsawa, et al.: "Behavior of the Bergman Kernel at infinity"Math, Zait.. (未定). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Asuke: "On the real secondary classes of transversely holomorphic foliations II"Tohoku Math.J.. 55. 361-274 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Asuke: "Localization and Residne of the Both class"Topolosy. 43. 289-317 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Suwa: "Residnes of Chern classes"J.Math.Soc.Japan. 55. 269-287 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Suwa: "Characteristic classes of singnlar varieties"Sugaku Expositions, AMS. 16. 153-175 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 中居 功: "WEB Geometry of solutions of Holonomic First Order PDEs"Natural Science Report, Ochanomizu Univ.. 52・1. 107-110 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 伊藤 敏和: "An application of the Cayley number to a holomorphic foliations on C^4"The Ryukoku Journal Humanities and Sciences. 24・1. 17-22 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 諏訪 立雄: "Residues of Chern Classes"J. Math. Soc. Japan. 55. 269-287 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 諏訪 立雄 他3名: "Milnor classes of local complete intersections"Trans Amer. Math. Soc.. 354. 1351-1371 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 武部 尚志: "A note on modified KP hierarchy and its (yet another)d's pereionle limit"Lett. Math. Phys.. 59. 157-172 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 足助 太郎: "Some results on secondary characteristic classee of transversely holomorphic foliations"Foliations : Geometry and Dynamics, world Scientific. 3-16 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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