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2003 Fiscal Year Final Research Report Summary

Construction of submanifolds via integrable systems

Research Project

Project/Area Number 12304005
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

SASAKI Takeshi  Kobe University, Faculty of Science, Professor, 理学部, 教授 (00022682)

Co-Investigator(Kenkyū-buntansha) OHNITA Yoshihiro  Tokyo Metropolitan University, Grad.School of Science, Professor, 大学院・理学研究科, 教授 (90183764)
SAKANE Yuusuke  Osaka University, Grad.School of Inform.Sci.Techn., Professor, 大学院・情報科学研究科, 教授 (00089872)
YOSHIDA Masaaki  Kyushu University, Grad.School of Math.Science, Professor, 大学院・数理学研究科, 教授 (30030787)
YAMAGUCHI Keizo  Hokkaido University, Grad.School of Science, Professor, 大学院・理学研究科, 教授 (00113639)
MIYAOKA Reiko  Kyushu University, Grad.School of Math.Science, Professor, 大学院・数理学研究科, 教授 (70108182)
Project Period (FY) 2000 – 2003
Keywordsgeometric structure / minimal surface / hypergeometric differential equation / integrable system / harmonic map constant / mean curvature surface / projective submanifold / line congruence
Research Abstract

The result of the project is summarized as follows :
1. Construction of a canonical projective immersion of the moduli space of marked cubic surfaces and determination of the uniformization equation
2. Study of shape of the image of Schwarz map defined by the Gauss differential equation with purely imaginary exponents
3. Study of transformations of projective surfaces such as projectively minimal surfaces and relation with line congruence and differential invariants; special surfaces defined by Appell's differential sytems
4. Computation of the harmonic cohomology of compact symplectic nilmanifolds and construction of distinct symplectic structures on such manifolds
5. Classification of CMC surfaces in H^3 and R^3 by the DPW method and explicit construction of discrete CMC surfaces
6. Determination of the condition that the mean curvature of rotation surface is periodic in terms of the integral of the mean curvature
7. Proposal of pluri-harmonic mapping of finite type making use of algebraic integrable systems
8. Formulation of variational problem of thin films under the gravity and study of stability of solutions
9. Unified method of solving sinh-Gordon, Liouville, and cosh-Gordon equation and construction of Backlund transformation of solutions
10. Implementation of prime decomposition of polynomial ideals over small finite fields
11. Introduction and study of the kappa function defined by j(k(r))=(r)
12. Definition of the notion of flat fronts for flat surfaces with singular points in 3-dimensional hyperbolic space and development of its theory
13. Proof of rigidity of projective immersions of Hermitian symmetric spaces not necessarily irreducible

  • Research Products

    (46 results)

All Other

All Publications (46 results)

  • [Publications] T.Sasaki: "The uniformizing differential equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces II"Journal of Physics A. 34. 2319-2328 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Yoshida: "A hyperbolic structure on the real locus of the moduli space of marked cubic surfaces"Topology. 40. 469-473 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Sasaki: "A genometric study of the hypergeometric function with imaginary exponents"Experimental Mathematics. 10. 321-330 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Mukai-Hidano: "Geometry of the moduli spaces of harmonic maps into Lie groups via gauge theory over Bjemann surfaces"International J.of Mathematics. 12. 339-371 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] P.Berard: "Index growth of hypersurfaces with constant mean curvature"Math.Zeitschr.. 239. 99-115 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Koiso: "Deformation and stability of surfaces with constant mean curvature"Tohoku Math.J.. 54. 145-159 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.Dorfmeister: "Weierstraβ-type representation of timelike surfaces with constant mean curvature"Contemporary Math., Amer.Math.Soc.. 308. 77-99 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Polthier: "Discrete constant mean curvature surfaces and their index"J.reine angew.Math.. 549. 47-77 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Ohnita: "Harmonic maps of finite type into generalized flag manifolds and twistor fibrations"Contemporary Mathematics, Amer.Math.Soc.. 308. 245-270 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] G.Ishikawa: "Submanifolds with degenerate Gauss mappings in the spheres"Advanced Studies in Pure Mathematics. 37. 115-149 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Noro: "An efficient modular algorithm for computing the global b-function"Proc of ICMS2002. 147-157 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Kajiwara: "_<10>E_9 solution to the elliptic Painleve equation"J.Phys.A. 36. 263-272 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Kenmotsu: "Surfaces of revolution with periodic mean curvature"Osaka Mathematical Journal. 40. 687-696 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Sasaki: "Invariant theory for linear differential systems modeled after Grassmannian Gr(n,2n)"Nagoya Mathematical Journal. 171. 163-186 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Sakane: "Harmonic forms on compact symplectic 2-step nilmanifolds"Geometry, integrability and quantization IV, STs.Constantine and Elena,2002. 257-270 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kaneko: "The kappa function"Internat.J.Math.. 14. 1003-1013 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] W.Rossman: "Mean curvature 1 surfaces in H^3 with low total curvature II"Tohoku Math.J.. 55. 375-395 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.Hwang: "Characterization of Hermitian symmetric spaces by fundamental forms"Duke Math.J.. 120. 621-634 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.Inoguchi: "Lorentz surfaces, timelike minimal surfaces and loop groups"Acta.Appl.Math. (未定)(to-appear). (2004)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Koiso: "Geometry and stability of bubbles with gravity"Indiana Univ.Math.J.. (未定)(to-appear). (2004)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Guest: "Contemporary Mathematics vols.308,309"Amer.Math.Soc.. 673 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 野呂正行: "グレブナー基底の計算 基礎篇 計算代数入門"東京大学出版会. xii+288 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Kenmotsu: "Surfaces with constant mean curvature"Amer.Math.Soc.. x+142 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Sasaki, M.Yoshida: "The uniformizing differential equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces II"Journal of Physics A. 34. 2319-2328 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Yoshida: "A hyperbolic structure on the real locus of the moduli space of marked cubic surfaces"Topology. 40. 469-473 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Sasaki, M.Yoshida: "A geometric study of the hypergeometric function with imaginary exponents"Experimental Mathematics. 10. 321-330 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Mukai-Hidano, Y.Ohnita: "Geometry of the moduli spaces of harmonic maps into Lie groups via gauge theory over Riemann surfaces"Intern.J.Math.. 12. 339-371 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Berard, L.L.de Lima, W.Rossman: "Index growth of hypersurfaces with constant mean curvature"Math Z.. 239. 99-115 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Koiso: "Deformation and stability of surfaces with constant mean Deformation and stability of surfaces with constant mean curvature"Tohoku Math.J.. 54. 145-159 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J.Dorfmeister, J.Inoguchi, M.Toda: "Weierstralss-type representation of timelike surfaces with constant mean curvature"Contemporary Mathematics, Amer.Math.Soc.. 308. 77-99 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Polthier, W.Rossman: "Discrete Constant Mean Curvature Surfaces and their Index"J.Reine.U.Angew.Math.. 549. 47-77 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Ohnita, S.Udagawa: "Harmonic maps of finite type into generalized flag manifolds and twistor fibrations"Contemporary Mathematics, Amer.Math.Soc.. 308. 245-270 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] G.Ishikawa, M.Kimura, R.Miyaoka: "Submanifolds with degenerate Gauss mappings in the spheres"Advanced Studies in Pure Mathematics. 37. 115-149 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Noro: "An efficient global modular algorithm for computing the global b-function"Proc of ICMS2002. 147-157 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada: "_<10>E_9 solution to the elliptic Painlevi equation"J.Phys.A. 36. L263-L272 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kenmotsu: "Surfaces of revolution with periodic mean curvature"Osaka Math.Jour.. 40. 687-696 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Sasaki, M.Yoshida: "Invariant theory for linear differential systems modeled after the Grassmannian Gr(n,2n)"Nagoya Math.J.. 171. 163-186 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Sakane, T.Yamada: "Harmonic forms on compact symplectic 2-step nilmanifolds"Geometry, integrability and quantization IV (Coral Press Sci.Publi., Sofia). 257-270 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Kaneko, M.Yoshida: "The kappa function"Internat J.Math.. 14. 1003-1013 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] W.Rossman, M.Umehara, K.Yamada: "Mean Curvature 1 Surfaces in H^3 with low total curvature II"Tohoku Math.J.. 55. 375-395 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J.Hwang, K.Yamaguchi: "Characterization of Hermitian symmetric spaces by fundamental forms"Duke Math.J.. 120. 621-634 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J.Inoguchi, M.Toda: "Lorentz surfaces, timelike minimal surfaces and loop groups"Acta.Appl.Math.. (to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Koiso, B.Palmer: "Geometry and Stability of Bubbles with Gravity"Indiana Univ.Math.J.. (to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Guest et al.(ed.): "Contemporary Mathematics vols.308, 309"Amer.Math.Soc.. 67 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Noro: "Gurebunakitei no keisan kisohen keisandaisuunyuumon"Tokyo Univ. xii+28 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kenmotsu: "Surfaces with constant mean curvature"Amer.Math.Soc.. x+142 (2003)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2005-04-19  

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