• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Research on Poisson manifolds and related structures on manifolds.

Research Project

Project/Area Number 09640088
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

MIZUTANI Tadayoshi  Saitama University, Dept.of Math., Professor, 理学部, 教授 (20080492)

Co-Investigator(Kenkyū-buntansha) FUKUI Toshizumi  Saitama Univ., Dept.of Math., Associate Professor, 理学部, 助教授 (90218892)
SAKURAI Tsutomu  Saitama Univ., Dept.of Math., Associate Professor, 理学部, 助教授 (40187084)
NAGASE Masayoshi  Saitama Univ., Dept.of Math., Professor, 理学部, 教授 (30175509)
SAKAMOTO Kunio  Saitama Univ., Dept.of Math., Professor, 理学部, 教授 (70089829)
OKUMURA Masafumi  Saitama Univ., Dept.of Math., Professor, 理学部, 教授 (60016053)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥1,800,000 (Direct Cost: ¥1,800,000)
KeywordsPoisson manifold / contact structure / Poisson cohomology / Schouten bracket / generalized divergence / symplectic foliation / leaf invariant / Dirac manifold / Hirsch foliation
Research Abstract

In the second year of the term of the project, we continued to investigate the prop- erties of the plane field which a 2-vector pi defines. A typical example of such plane field is the tangentially symplectic foliation associated with a Poisson structure. In the course of investigation, we obtained the following new insight. (1) In the first year, we showed ; when dim M = 2kappa + 1, if [pi, pi^<kappa>]<double plus> 0, pi defines a contact plane field. This time we have proved the existence of a connection of M such that Divpi (w.r.t. this connection) is a Reel) vector field of the contact structure. (2) If pi defines a (regular) Poisson sturcture, Divpi is a Poisson 1-cocycle and is the image of a modular class (= h_1 in the usual notation of characteristic classes) of the associated folation.
This result suggest the possibility of the definition of characteristic classes of singular foliations in terms of Poisson structures in some cases. As a first attempt in this direction, we picked up the left in variant Poisson structures of Lie groups and tried. to descripe the 3-dimensional leaf invarinat (h_3). In a. different direction of singular objects, we studied Dirac structure on manifoIds. A little more time is needed for us to unite these studies arid obtain adenite results.

Report

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

    (26 results)

All Other

All Publications (26 results)

  • [Publications] M.Djore and Okumura: "CR submanifolds of maximal CR dimension of complex projective space" Arehiv der Mathematik. 71. 148-158 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Sakamoto: "On the curvature of minimal 2-spheres in spheres" Math. Zeitschrift. 228. 605-627 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Nagase: "Spin^q, twistor and Spin^c" Commun. Math. Phys.189. 107-126 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Fukui: "Seeking invariants for blow-analytic equivalence" Compositio Math.105. 95-108 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Fukui, S.Koike, T.C.Kuo: "Blow-analytic equi-singularities, properties, problems and progress" Pitman Research Notes. in Math. Series, Longman. 381. 8-29 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Fukui: "Newton polygons and topology of real zero loci of real polynomials" Journal of London Mathematical Society. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Djorc and M.Okumura: "CR submanifolds of maximal CR dimension of complex projective space" Archiv der Mathematik. 71. 148-158 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Sakamoto: "On the curvature of minimal 2-spheres in spheres" Math.Zeitschrift. 228. 605-627 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Nagase: "Spin^q, twistor and Spin^c" Commun.Math.Phys.189. 107-126 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Fukui: "Seeking invariants for blow-analytic equivalence" Compositio Math.105. 95-108 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Fukui: "S.Koike, T.C.Kuo, Blow-analytic equisingularities, properties, problems and progress" Pitman Research Notes in Math.Series, Longman. 381. 8-29 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Fukui: "Newton polygons and topology of real zero loci of real polynomials" Journal of London Mathematical Society. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Fukui, J.Nuno Ballesteros, M.Saia: "On the number of singularities in generic deformations of mapgerms" Journal of London Mathematical Society. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Shinji Egashira: "Qualitative theory and expansion growth of transversely piecewise-smooth foliated S^1-bundles" Ergod.Th.& Dynam.Sys.17. 331-347 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Djorc and Okumura: "CR submanifolds of maximal CR dimension of complex projective space" Archiv der Mathematik. 71. 148-158 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Sakamoto: "On the curvature of minimal 2-spheres in spheres" Math.Zeitschrift. 228. 605-627 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Nagase: "Spin^q,twistor and Spin^c" Commun.Math.Phys.189. 107-126 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Fukui: "Seeking invariants for blow-analytic equivalence" Compositio Math.105. 95-108 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Fukui,S.Koike,T.C.Kuo: "Blow-analytic equi-singularities,propeties,problems and progress" Pitman Research Notes.in Math.Series,Longman. 381. 8-29 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Fukui: "Newton polygons and topology of real zero loci of real polynomials" Journal of London Mathematical Society,to appear.

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Djorc and Okumura: "CR submanifolds of maximal CR dimension of complex projective space" Archiv der Mathematik. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Sakamoto: "On the curvature of minimal 2-spheres in spheres" Math. Zeitshrift. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Fukui: "Seeking invariants for blow-analytic equivalence" Compositio Math.105. 95-108 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Fukui, S.Koike, T.C.Kuo: "Blow-analytic equi-singularities, propeties, problems and progress" Pitman Research Notes. in Math.Series, Longman. 381. 8-29 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Fukui: "Newton polygons and topology of real zero loci of real polynomials" Journal of London Mathematical Society. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] T.Fukui, J.Nuno Ballesteros, M.Saia: "On the number of singularities in generic deformations of map germs" Journal of London Mathematical Society. (to appear).

    • Related Report
      1997 Annual Research Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi