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2005 Fiscal Year Final Research Report Summary

Geometry and topology of integrable systems, with computer-aided experimentation and visualization

Research Project

Project/Area Number 14204005
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo Metropolitan University

Principal Investigator

GUEST Martin  Tokyo Metropolitan University, Faculty of Urban Liberal Arts, Professor, 都市教養学部, 教授 (10295470)

Co-Investigator(Kenkyū-buntansha) OHNITA Yoshihiro  Osaka City University, Graduate School of Science, Professor, 理学研究科, 教授 (90183764)
MIYAOKA Reiko  Kyushu University, Faculty of Mathematics, Professor, 数理学研究院, 教授 (70108182)
OTOFUJI Takashi  Nihon University, College of Engineering, Lecture, 工学部, 講師 (70339266)
HAMADA Tatsuyoshi  Fukuoka University, Faculty of Science, Assistant, 理学部, 助手 (90299537)
Project Period (FY) 2002 – 2005
KeywordsGeometry / Topology / Integrable systems / Quantum cohomology / Computer experiments / Visualization
Research Abstract

Research problems in geometry and topology were investigated using methods from the theory of integrable systems. These included research on the classification of constant mean curvature (CMC) surfaces, isoparametric manifolds, Lagrangian submanifolds, harmonic maps, and quantum cohomology. The principal investigator obtained results on the D-module structure of quantum cohomology, and began a systematic study of relations between quantum cohomology and integrable systems.
Computer experiments played an important role in this project. MAPLE was used for computations with differential operators and differential equations, 3D-XplorMath was used for lattice model simulations, and CMC-Lab was used to study CMC surfaces. Several domestic and international research conferences were supported or partially supported, concentrating on the theme of "geometry and visualization". New techniques of computer experimentation and visualization were introduced at these conferences by researchers from Germany and the USA.
Dissemination and promotion of such computer techniques in Japan was an important goal of this project. The Research Assistant and several investigators wrote Japanese documentation and demonstrated software at conferences. Two websites were developed as part of this project : "geom" (for the Geometry Section of the Mathematical Society of Japan), and "tmugs" (for geometry research activities in the Tokyo Metropolitan area). Three "computer tutorials" were held towards the end of the project period. These tutorials were based on experience gained during the project, and will serve as a model for future development of this research area and associated human resources in Japan.

  • Research Products

    (63 results)

All 2005 2004 2003 2002

All Journal Article (62 results) Book (1 results)

  • [Journal Article] Quantum cohomology via D-modules2005

    • Author(s)
      Martin Guest
    • Journal Title

      Topology 44

      Pages: 263-281

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Gromov-Witten invariants of flag manifolds, via $D$-modules2005

    • Author(s)
      Amarzaya, A., Guest, M.A
    • Journal Title

      J.London Math.Soc 72

      Pages: 121-136

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On Alexander polynomials of torus curves2005

    • Author(s)
      Audoubert, Benoit, Nguyen, Tu Chanh, Oka, Mutsuo
    • Journal Title

      J.Math. Soc. Japan 57

      Pages: 935-957

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On Fermat curves and maximal nodal curves2005

    • Author(s)
      Oka, Mutsuo
    • Journal Title

      Michigan Math. J 53

      Pages: 459-477

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the fundamental groups of the complements of plane singular sextics2005

    • Author(s)
      Eyral, Christophe, Oka, Mutsuo
    • Journal Title

      J.Math.Soc.Japan 57

      Pages: 37-54

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] $N=frac 12$ supersymmetric four-dimensional nonlinear $sigma$-models from nonanticommutative superspace2005

    • Author(s)
      Hatanaka, Tomoya, Ketov, Sergei V., Kobayashi, Yoshishige, Sasaki, Shin
    • Journal Title

      Nuclear Phys.B 726

      Pages: 481-493

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] ${rmSU}(2)times{rmU}(1)$nonanticommutative$N=2$supersymmetric gauge theory2005

    • Author(s)
      Ketov, Sergei V., Sasaki, Shin
    • Journal Title

      Internat.J.Modern Phys.A 20

      Pages: 4021-4034

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Summing up non-anticommutative Kahler potential2005

    • Author(s)
      Hatanaka, Tomoya, Ketov, Sergei V., Sasaki, Shin
    • Journal Title

      Phys.Lett.B 619

      Pages: 352-358

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Non-anti-commutative deformation of effective potentials in supersymmetric gauge theories2005

    • Author(s)
      Hatanaka, Tomoya, Ketov, Sergei V., Kobayashi, Yoshishige, Sasaki, Shin
    • Journal Title

      Nuclear Phys.B 716

      Pages: 88-104

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Intersection theory for Lagrangian immersions2005

    • Author(s)
      Akaho, Manabu
    • Journal Title

      Math.Res.Lett 12

      Pages: 543-550

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Yang-Mills fields analogue of biharmonic maps2005

    • Author(s)
      Bejan, Cornelia-Livia, Urakawa, Hajime
    • Journal Title

      World Sci.Publ., Hackensack,NJ

      Pages: 41-49

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The first bifurcation point for Delaunay nodoids2005

    • Author(s)
      Rossman, Wayne
    • Journal Title

      Experiment.Math 14

      Pages: 331-342

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Constructing mean curvature 1 surfaces in $Hsp 3$ with irregular ends2005

    • Author(s)
      Rossman, Wayne, Umehara, Masaaki, Yamada, Kotaro
    • Journal Title

      Clay Math.Proc 2

      Pages: 561-584

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Constant mean curvature surfaces of any positive genus2005

    • Author(s)
      Kilian, M., Kobayashi, S.P., Rossman, W., Schmitt,N
    • Journal Title

      J.London Math.Soc 72

      Pages: 258-272

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Ruled real hypersurfaces in a nonflat quatemionic space form2005

    • Author(s)
      Adachi, Toshiaki, Maeda, Sadahiro, Udagawa, Seiichi
    • Journal Title

      Monatsh.Math 145

      Pages: 179-190

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Pseudo-symmetric contact 3-manifolds2005

    • Author(s)
      Cho, Jong Taek, Inoguchi, Jun-Ichi
    • Journal Title

      J.Korean Math.Soc 42

      Pages: 913-932

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Flat translation invariant surfaces in the 3-dimensional Heisenberg group2005

    • Author(s)
      Inoguchi, Jun-ichi
    • Journal Title

      J.Geom 82

      Pages: 83-90

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Grassmann geometry on the 3-dimensional Heisenberg group2005

    • Author(s)
      Inoguchi, Jun-ichi, Kuwabara, Kenji, Naitoh, Hiroo
    • Journal Title

      Hokkaido Math.J 34

      Pages: 375-39

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Real hypersurfaces of complex space forms with symmetric Ricci $^*$-tensor2005

    • Author(s)
      Hamada, Tatsuyoshi, Inoguchi, Jun-Ichi
    • Journal Title

      Mem.Fac.Sci.Eng.Shimane Univ.Ser.B Math.Sci 38

      Pages: 1-5

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Characterizations of Bianchi-Backlund transformations of constant mean curvature surfaces2005

    • Author(s)
      Kobayashi, Shimpei, Inoguchi, Jun-Ichi
    • Journal Title

      Internat.J.Math 16

      Pages: 101-110

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Gromov-Witten invariants of flag manifolds, via $D$-modules.2005

    • Author(s)
      Amarzaya.A, Guest.M.A
    • Journal Title

      J. London Math.Soc 72

      Pages: 121-136

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On Alexander polynomials of torus curves2005

    • Author(s)
      Audoubert.Benoit, Nguyen.Tu Chanh, Oka.Mutsuo
    • Journal Title

      J.Math.Soc.Japan 57

      Pages: 935-957

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On Fermat curves and maximal nodal curves2005

    • Author(s)
      Oka.Mutsuo
    • Journal Title

      Michigan Math.J 53

      Pages: 459-477

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On the fundamental groups of the complements of plane singular sextics2005

    • Author(s)
      Eyral.Christophe, Oka.Mutsuo
    • Journal Title

      J.Math.Soc.Japan 57

      Pages: 37-54

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] $N=frac 12$ supersymmetric four-dimensional nonlinear $sigma$-models from nonanticommutative superspace2005

    • Author(s)
      Hatanaka.Tomoya, Ketov.Sergei V, Kobayashi.Yoshishige, Sasaki.Shin
    • Journal Title

      Nuclear Phys.B 726

      Pages: 481-493

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] ${rm SU}(2)times {rm U}(1)$ nonanticommutativte $N=2$ supersymmetric gauge theory2005

    • Author(s)
      Ketov.Sergei V, Sasaki.Shin
    • Journal Title

      Internat.J.Modern Phys.A 20

      Pages: 4021-4034

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Summing up non-anticommutative Kahler potential2005

    • Author(s)
      Hatanaka.Tomoya, Ketov.Sergei V, Sasaki.Shin
    • Journal Title

      Phys.Left.B 619

      Pages: 352-358

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Non-anti-commutative deformation of effective potentials in supersymmetric gauge theories2005

    • Author(s)
      Hatanaka.Tomoya, Ketov.Sergei V, Kobayashi.Yoshishige.Sasaki.Shin
    • Journal Title

      Nuclear Phys.B 716

      Pages: 88-104

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Intersection theory for Lagrangian immersions2005

    • Author(s)
      Akaho.Manabu
    • Journal Title

      Math.Res.Left 12

      Pages: 543-550

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Yang-Mills field: analogue of biharmonic maps.2005

    • Author(s)
      Bejan.Comelia-Livia, Urakawa.Hajime
    • Journal Title

      World Sci.Publ., Hackensack, NJ

      Pages: 41-49

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The first bifurcation point for Delaunay nodoids.2005

    • Author(s)
      Rossman. Wayne
    • Journal Title

      Experiment.Math 14

      Pages: 331-342

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Constructing mean curvature 1 surfaces in $Hsp 3$ with irregular ends2005

    • Author(s)
      Rossman.Wayne, Umehara.Masaaki.Yamada.Kotaro
    • Journal Title

      Clay Math.Proc 2

      Pages: 561-584

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Constant mean curvature surfaces of any positive genus2005

    • Author(s)
      Kilian.M, Kobayashi.S.-P, Rossman, W, Schmitt, N
    • Journal Title

      J.London Math.Soc 72

      Pages: 258-272

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Ruled real hypersurfaces in a nonflat quaternionic space form.2005

    • Author(s)
      Adachi.Toshiaki, Maeda.Sadahiro, Udagawa.Seiichi
    • Journal Title

      Monatsh.Math 145

      Pages: 179-190

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Pseudo-symmetric contact 3-manifolds.2005

    • Author(s)
      Cho.JongTaek, Inoguchi.Jun-Ichi
    • Journal Title

      J.Korean Math.Soc 42

      Pages: 913-932

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Flat translation invariant surfaces in the 3-dimensional Heisenberg group2005

    • Author(s)
      Inoguchi.Jun-ichi
    • Journal Title

      J.Geom 82

      Pages: 83-90

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Grassmann geometry on the 3-dimensional Heisenberg group2005

    • Author(s)
      Inoguchi.Jun-ichi, Kuwabara.Kenji, Naitoh.Hiroo
    • Journal Title

      Hokkaido Math.J 34

      Pages: 375-39

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Real hypersurfaces of complex space forms with symmetric Ricci $*$-tensor.2005

    • Author(s)
      Hamada.Tatsuyoshi, Inoguchi.Jun-Ichi
    • Journal Title

      Mem.Fac.Sci.Eng.Shimane Univ.Ser.B Math.Sci 38

      Pages: 1-5

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Characterizations of Bianchi-Backlund transformations of constant mean curvature surfaces2005

    • Author(s)
      Kobayashi.Shimpei, Inoguchi.Jun-Ichi
    • Journal Title

      Internat.J.Math 16

      Pages: 101-110

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Yang-Mills theory over compact symplectic manifolds2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Annals Global Analysis Geometry 25

      Pages: 365-402

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Timelike minimal surfaces via loop groups2004

    • Author(s)
      J.Inoguchi, M.Toda
    • Journal Title

      Acta Appl.Math 83

      Pages: 313-355

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Constructions of almost complex 2-tori of type (III)in the nearly Kaehler 6-sphere2004

    • Author(s)
      S.Udagawa, H.Hashimoto, T.Taniguchi
    • Journal Title

      Differential Geom.Appl 21

      Pages: 127-145

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Constructions of almost complex 2-tori of type (III) in the nearly Kaehler 6-sphere2004

    • Author(s)
      S.Udagawa, H.Hashimoto, T.Taniguchi
    • Journal Title

      Differential Geom.Appl 21

      Pages: 127-145

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces2003

    • Author(s)
      Y.Ohnita, A.Amarzaya
    • Journal Title

      Tohoku Math J 55

      Pages: 583-610

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Geometry of reduced sextics of torus type2003

    • Author(s)
      M.Oka
    • Journal Title

      Tokyo J.Math 55

      Pages: 301-327

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Variation of toric hyperkahler manifolds2003

    • Author(s)
      H.Konno
    • Journal Title

      Intermat.J.Math 14

      Pages: 289-311

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Integral Geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in s^2 times s^22003

    • Author(s)
      T.Sakai, H.Irieh, H.Ono
    • Journal Title

      Proc.Japan Acad 79

      Pages: 167-170

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces2003

    • Author(s)
      Y.Ohnita, A.Amarzaya
    • Journal Title

      Tohoku Math J. 55

      Pages: 583-610

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Geometry of reduced sextics of torus type2003

    • Author(s)
      M.Oka
    • Journal Title

      Tokyo J.Math. 55

      Pages: 301-327

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Variation of toric hyperkahler manifolds2003

    • Author(s)
      H.Konno
    • Journal Title

      Internat.J.Math 14

      Pages: 289-311

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Integral Geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in S^2 times S^22003

    • Author(s)
      T.Sakai, H.Irieh, H.Ono
    • Journal Title

      Proc.Japan Acad 79

      Pages: 167-170

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Submanifolds with degenerate Gauss mappings in the sphere2002

    • Author(s)
      G.Ishikawa, M.Kimura, R.Miyaoka
    • Journal Title

      Advanced Siudies in Pure Mathematics 37

      Pages: 115-149

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Discrete Constant Mean Curvature Surfaces and their Index2002

    • Author(s)
      W.Rossman
    • Journal Title

      J.Reine uAngew Math 549

      Pages: 47-77

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Lower bounds for Morse index of constant mean curvaturetori2002

    • Author(s)
      W.Rossman
    • Journal Title

      Bull.London Math.Soc 34

      Pages: 211-218

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Discrete Conjugate Nets of strings2002

    • Author(s)
      S.Saito, N.Suzuki, H.Ymaguchi
    • Journal Title

      Contemporary Mathematics 309

      Pages: 199-209

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Quantum cohomology of infinite dimensional flag2002

    • Author(s)
      T.Otofuji
    • Journal Title

      Contemporary Mathematics 309

      Pages: 199-209

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Conformally geometric viewpoints for knots and links I2002

    • Author(s)
      R.Iangevin, J.Ohara
    • Journal Title

      Contemporary Mathematics 304

      Pages: 187-194

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Submanifolds with degenerate Gauss mappings in the spheres2002

    • Author(s)
      G.Ishikawa, M.Kimura, R.Miyaoka
    • Journal Title

      Advanced Siudies in Pure Mathematics 37

      Pages: 115-149

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Discrete Constant Mean Curvature Surface and their Index2002

    • Author(s)
      W.Rossman
    • Journal Title

      J.Reine u Angew Math 549

      Pages: 47-77

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Discrete Conjugate Nets of Strings2002

    • Author(s)
      S.Saito, N.Suzuki, H.Ymaguchi
    • Journal Title

      Contemporary Mathematics 309

      Pages: 199-209

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Quantum cohomology of infinite dimensional flag manifolds2002

    • Author(s)
      T.Otofuji
    • Journal Title

      Contemporary Mathematics 309

      Pages: 199-209

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Conformally geometric viewpoints for knots and links I2002

    • Author(s)
      R.langevin, J.Ohara
    • Journal Title

      Contemporary Mathematics 304

      Pages: 187-194

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] Integrable systems, Topology, and Physics2002

    • Author(s)
      M.Guest, R.Miyaoka, Y.Ohnita
    • Total Pages
      324
    • Publisher
      Amer.Math.Soc
    • Description
      「研究成果報告書概要(和文)」より

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Published: 2007-12-13  

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