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

Research on global structures of Lorentzian semi-symmetric spaces

Research Project

Project/Area Number 16540089
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionFukuoka Institute of Technology

Principal Investigator

GOTO Midori  Fukuoka Institute of Technology, Information Engineering, Professor, 情報工学部, 教授 (60162161)

Co-Investigator(Kenkyū-buntansha) SUGAHARA Kunio  Osaka Kyoiku University, Education, Professor, 教育学部, 教授 (20093255)
NISHIHARA Masaharu  Fukuoka Institute of Technology, Information Engineering, Professor, 情報工学部, 教授 (20112287)
NISHIYAMA Takahiro  Yamaguchi University, Graduate School of Science and Engineering, Associate Professor, 大学院理工学研究科, 助教授 (60333241)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsLorentzian metric / Lorentz manifold / semi-symmetric space / Liouville metric / Liouville manifold / Liouville surface / generalized Liouville manifold / Lorentz-Liouville構造 / Liouville構造 / generalized-Liouville構造 / ローレンツ型擬対称空間 / 局所共形平坦 / ローレンツ曲面 / 共形平坦 / 大域的構造 / リッチ曲率
Research Abstract

In the study of Riemannian geometry, it is important to investigate geodesic behaviors, which effect on topological structures of manifolds. Curvatures (local notion) of Riemannian manifolds often have influence on topological structures (global notion). What about in Lorentz geometry? From the viewpoints, we investigate Lorentz geometry. Global behaviors of geodesics are not well-known for most manifolds. Hence, investigations of Liouville structure, which have been initiated by C.G.F.Jacobi in 1866, turn out to be important.
Our main results which we obtained during the period are in the following two forthcoming papers, both of which are joint works by Midori Goto and Kunio Sugahara :
1. Generalized Liouville manifolds.
In this paper, we defined a new notion, the generalized Liouville structure, and succeeded to prove that all quadric surfaces in the n+1 dimensional Cartesian space possess the generalized Liouville structures with respect to the indefinite/definite metrics, besides the Eucledian metric. In the classification of Riemann-Liouville surfaces the number of singularities plays a key role in Kiyohara's and Igarashi-Kiyohara-Sugahara's papers about Liouville surfaces. We proved that there is no such kind of singularity in the Lorentz-Liouville surface. For generalized Liouville maniflods of dimension >2, we determined the set of singularities. The classification problems for generalized Liouville manifolds are supposed to be made clear.
2. A remark on Lorentzian metrics of 3-dimensional manifolds.
In the paper, we see that there are 3-dimensional Riemannian manifolds whose Riemannian connections coincide with the Lorentzian connections associated with the naturally defined Lorentzian metrics. Reviewing the result, we conjecture that, except for the case of constant curvature, there may not be expected any relations between curvatures and topological structures.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (26 results)

All 2007 2006 2005 2004 Other

All Journal Article (24 results) Book (2 results)

  • [Journal Article] An integral transform whose kernel is a stream function of a steady Euler flow with axisymmetry2007

    • Author(s)
      Takahiro Nishiyama
    • Journal Title

      Z. Angew. Math. Phys. 58

      Pages: 68-80

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An integral transform whose kernel is a stream function of a steady Euler flow with axisymmetry2007

    • Author(s)
      Takahito Nishiyama
    • Journal Title

      Z. Angew. Math. Phys. 58

      Pages: 68-80

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An integral transform whose kernel is a stream function of a steady Euler flow with axisymmetry2007

    • Author(s)
      西山 高弘
    • Journal Title

      Z.Agnew Math.Phys. 58

      Pages: 68-80

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Global structures of compact conformally flat semi-symmetric spaces of dimension 3 and of non-constant curvature2006

    • Author(s)
      Midori S. Goto
    • Journal Title

      Progress in Mathematics, Birkhauser 252

      Pages: 69-83

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A note on Lorentz metrics of 3-dimensional conformally flat manifolds2006

    • Author(s)
      Midori S. Goto
    • Journal Title

      Res. Bull. F. I. T. 38・2

      Pages: 149-152

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A relaxation method for construction a Beltrami flow in a bounded domain2006

    • Author(s)
      Takahiro Nishiyama
    • Journal Title

      J. Math. Phys. 46・8

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global structures of compact conformally flat semi-symmetric spaces of dimension 3 and of non-constant curvature2006

    • Author(s)
      Midori S. Goto
    • Journal Title

      Progress in Mathematics 252

      Pages: 69-83

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A note on Lorentz metrics of 3-dimensional conformally flat manifolds2006

    • Author(s)
      Midori S. Goto
    • Journal Title

      Res. Bull. F. I. T. 38-2

      Pages: 149-152

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A relaxation method for construction a Beltrami flow in a bounded domain2006

    • Author(s)
      Takahiro Nishiyama
    • Journal Title

      J. Math. Phys. 46-8

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Global structures of compact conformally flat semi-symmetric spaces of dimension 3 and of non-constant curvature2006

    • Author(s)
      後藤 ミドリ
    • Journal Title

      From Geometry to Quantum mechanics, Progress in Math. 252

      Pages: 69-83

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A note on Lorentzian metrics of 3- dimensional conformally flat manifolds2006

    • Author(s)
      後藤ミドリ
    • Journal Title

      Res.Bull.F.I.T 38・2

      Pages: 149-152

    • Related Report
      2006 Annual Research Report
  • [Journal Article] a note on Lorentzian metrics of 3-dimensional conformally flat manifolds2006

    • Author(s)
      後藤 ミドリ
    • Journal Title

      Res.Bull.F.I.T. 38・2

      Pages: 149-152

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Construction of axisymmetric steady states of an inviscid incompressible fluid by apatially discretized equations for psudo-advected vorticity2005

    • Author(s)
      Takahiro Nishiyama
    • Journal Title

      Int. J. Math. and Math. Sci. 2005・20

      Pages: 3319-3346

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Construction of axisymmetric steady states of an inviscid incompressible fluid by apatially discretized equations for psudo-advected vorticity2005

    • Author(s)
      Takahiro Nishiyama
    • Journal Title

      Int. J. Math. and Math. Sci. 2005-20

      Pages: 3319-3346

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On the extension of holomorphic mappings on nuclear spaces2005

    • Author(s)
      西原 賢
    • Journal Title

      Proc.The.12^<th> International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, 2004・July27-31

      Pages: 245-252

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A relaxation method for constructing a Beltrami flow in a bounded domain2005

    • Author(s)
      西山 高弘
    • Journal Title

      J.Math.Phys. 46・8

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Construction of axisymmetric steady states of an inviscid incompressible fluid by spatially disally discretized equations for pseudo-advected vorticity2005

    • Author(s)
      西山 高弘
    • Journal Title

      Int.J.Math.Sci. 2005・20

      Pages: 3319-3346

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A Hahn-Banach extension theorem for entire functions of nuclear type2004

    • Author(s)
      西原 賢
    • Journal Title

      J.Korean Math.Soc. 41

      Pages: 131-143

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The Frenkel's lemma in Banach spaces and its applications2004

    • Author(s)
      西原 賢 他4名
    • Journal Title

      Far East J.Math.Sci. 14

      Pages: 69-93

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Magnetohydrodynamics approaches to measure-valued solutions of the two-dimensional stationary Euler equations

    • Author(s)
      Takahiro Nishiyama
    • Journal Title

      Bull. Inst. Math. Sinica (New Series) (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Magnetohydrodynamics approaches to measure-valued solutions of the two-dimensional stationary Euler equations

    • Author(s)
      Takahiro Nishiyama
    • Journal Title

      Bull. Inst. Math. Sinica (New Series) (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Magnetohydrodynamic approaches to measure-valued solution of the two-dimensional stationary Euler equations

    • Author(s)
      西山 高弘
    • Journal Title

      Bull.Inst.Math.Sinica(New Ser.) 印刷中

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Global structures of compact conformally flat semi-symmetric spaces of dimension three and of non-constant curvature

    • Author(s)
      後藤 ミドリ
    • Journal Title

      Birkhauser社、Progress in Math.シリーズ 印刷中

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Magnetohynamic approaches to measure-valued solutions of the two-dimensional stationary Euler equations

    • Author(s)
      西山 高弘
    • Journal Title

      Transport Theory Statist.Phys. 印刷中

    • Related Report
      2005 Annual Research Report
  • [Book] 微分幾何の基本概念(J.A. Thorpe著、 Elementary Topics in Differential Geometryの翻訳書)2006

    • Author(s)
      後藤ミドリ 他2名
    • Total Pages
      405
    • Publisher
      シュプリンガー・フェアラーク東京
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Book] 微分幾何の基礎概念2006

    • Author(s)
      後藤ミドリ, 石川普, 糸川銚
    • Total Pages
      405
    • Publisher
      シュプリンガー・フェアラーク東京
    • Related Report
      2006 Annual Research Report

URL: 

Published: 2004-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi