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DIFFERENTIAL GEOMETRIC RESEARCH ON SUBMANIFOLDS AND STUDY OF SYSTEMS FOR THE EFFECTIVE DISSEMINATION OF RESEARCH

Research Project

Project/Area Number 09440038
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTOKYO METROPOLITAN UNIVERSITY

Principal Investigator

OGIUE Koichi  GRADUATE SCHOOL OF SCIENCE, DEPARTMENT OF MATHEMATICS, TOKYO METROPOLITAN UNIVERSITY, PROFESSOR, 大学院・理学研究科, 教授 (10087025)

Co-Investigator(Kenkyū-buntansha) MAEDA Sadahiro  DEPARTMENT OF MATHEMATICS, SHIMANE UNIVERSITY, PROFESSOR, 総合理工学部, 教授 (40181581)
NAKAMULA Ken  FACULTY OF SCIENCE, DEPARTMENT OF MATHEMATICS, TOKYO METROPOLITAN UNIVERSITY, PROFESSOR, 大学院・理学研究科, 教授 (80110849)
OHNITA Yoshihiro  GRADUATE SCHOOL OF SCIENCE, DEPARTMENT OF MATHEMATICS, TOKYO METROPOLITAN UNIVERSITY, PROFESSOR, 大学院・理学研究科, 教授 (90183764)
KENMOTSU Katsuei  MATHEMATICAL INSTITUTE, TOHOKU UNIVERSITY, PROFESSOR, 理学研究科, 教授 (60004404)
UDAGAWA Seiichi  DEPARTMENT OF MATHEMATICS, SCHOOL OF MEDICINE, NIHON UNIVERSITY, LECTURER, 医学部, 講師 (70193878)
濱田 龍義  福岡大学, 理学部, 助手 (90299537)
塩浜 勝博  佐賀大学, 理工学部, 教授 (20016059)
塚田 和美  お茶の水女子大学, 理学部, 教授 (30163760)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥11,900,000 (Direct Cost: ¥11,900,000)
Fiscal Year 1998: ¥5,300,000 (Direct Cost: ¥5,300,000)
Fiscal Year 1997: ¥6,600,000 (Direct Cost: ¥6,600,000)
KeywordsSubmanifold / Differential Geometry / Curve / Surface / Curvature / System for dissemination of research / 情報交換システム / 部分多様体 / 平均曲率 / 極小曲面 / 可積分系 / 調和写像 / Gauss写像 / 曲面上の曲線 / 可積分素
Research Abstract

Differential Geometry is originated to the study of curves and surfaces in 3-dimensional Euclidian space and submanifold theory is a central research subject. One of this research project is to develop the differential geometric research of submanifolds and the study of its realted branches. Another is to construct and to work the systems for the effective dissemination of research in this field. In 1997, after the head investigator and investigators discussed working plans and made a setting of research aims and a choice of priority items in each division of project, and organized research groups led by each investigators, we started the research activities. First, in order to enable us effective exchange of informations, Nakamula and Hamada led to construct a mailing system and to start a use of the system. At present, 246 researchers of this area in the world belong to the system. In order to report research results in the environs of each investigators and to obtain informations fr … More om neighboring areas, we organized 4 conferences in 1997 and 4 conferences in 1998. They are extremely important on step up our research. Especially conferences inviting foreign researchers had much effect on enlarging our view. It was very advantageous that investigators joined international conferences outside the country and gave talks on their research results, and they were able to have information exchange with many foreign mathematicians. As results of these activities, Ogiue, Maeda, Adachi, Udagawa and others greatly contributed to give so many results in the study of curves (closed geodesics, circles, helixes) in specific Riemanninan manifolds and their submanifolds. Concerned with the study of surfaces and real hypersurfaces in spheres and complex projective spaces, Maeda, Takagi, Kitagawa and others provided many deep results. Strikingly, Miyaoka provided a wonderful progress in the classification problem since E. Cartan of isoparametric hypersurfaces in spheres, and Kenmotsu provided a big progress in the classification problem since E. Cartan of minimal surfaces with constant Gaussian curvature in complex projective spaces beginning from S.S. Chern's work. In the study of harmonic maps of Riemann surfaces into symmetric spaces and their realted minimal surfaces, Ejiri, Ohnita, Udagawa and others gaves several progress from the viewpoint of theory of integrable systems. From the viewpoint of singularity theory, knot theory, gauge theory, moduli spaces etc. and other neighboring branches, Izumiya, Ohara, Ohnita and others worked on this research project and gave new results. Based on these results of this project, we greatly expect the further progress of this area. Less

Report

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

    (39 results)

All Other

All Publications (39 results)

  • [Publications] S.Maeda: "Length spectrum of circles in a complex projective space"Osaka J.Math. 35. 553-565 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Ogiue: "Characterizations of geodesic hyperspheres in a complex projective space by observing the extrinsic shape of geodesics"Math.Z.. 225. 537-542 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Ejiri: "The boundary of the space of full harmonic maps of S^2 into S^<2m> and extra eigenfunctions"Japanese J.Math. 24. 83-121 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Kitagawa: "An n-dimensional flat torus in S^3 whose extrinsic diameter is equal to π"Kodai Math.J.. 20. 156-160 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Ohnita: "Actions of loop groups, deformations of harmonic maps, and their application's"Amer.Math.Soc, Translations Ser.2. 183. 33-50 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] R.Takagi: "The rigidity for real hypersurfaces in a complex projective space"Tohoku Math.J.. 50. 531-536 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 荻上紘一: "共立講座・21世紀の数学「多様体」"共立出版. 220 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S. Maeda: "Length spectrum of circles in a complex projective space"Osaka J. Math.. 35. 553-565 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K. Ogiue: "Characterizations of geodesic hyperspheres in a complex projective space by obwerving the extrinsic shape of geodesics"Math. Z.. 225. 537-542 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N. Ejiri: "The boundary of the space of full harmonic maps of S^2 into S^2m and extra eigenfunctions"Japanese J. Math.. 24. 83-121 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y. Kitagawa: "An n-dimensional flat torus in S^3 whose extrinsic diameter is equal to \pi"Kodai Math. J.. 20. 156-160 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y. Ohnita: "Actions of loop groups, deformations of harmonic maps, and their applications"Amer. Math. Soc. Translations Ser.2. 183. 33-50 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] R. Takagi: "The rigidity for real hypersurfaces in a complex projective space"Tohoku Math. J.. 50. 531-536 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 荻上紘一: "On 3-dimensional isotropic submanifolds of a-space form" Turkish J.Math.発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 大仁田義裕: "Gauge-theoretic equations for symmetric spaces …" Proc.Int.Conf.held at Brest. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 宮岡礼子: "The splitting and deformations of the …" Tohoku Math.J.51. 35-53 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 大原 淳: "Asymptotic formulae of energies of …" Proc.Conf.Low Dim.Top.発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 足立俊明: "Length spectrum of circles …" Osaka J.Math.35. 553-565 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 濱田龍義: "On real hypersurfaces of a complex …" Glasgow Math.J.(1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 塩浜勝博: "Conformally flat 3-manifolds in …" J.Math.Soc.Japan. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 泉屋周一: "A time-like surface in Minkowski …" J.Geometry. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 江尻典雄: "The boundary of the space of …" Japanese J.Math.24. 83-121 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 宇田川誠一: "Simpleness and closedness of circles …" 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 前田定広: "A construction of closed helices …" Hokkaido Math.J.発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 高木亮一: "The rigidity for real hypersurfaces …" Tohoku Math.J.50. 531-536 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 大仁田・宮岡: "調和写像と可積分系理論" 裳華房, (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 荻上 紘一: "Characterizations of geodesic hyperspheres in a complex projective space by doserving the extrinsic shape of geodesics" Math.Z. 225. 537-542 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 塚田 和美: "Holomorphic maps of compact generalized Hopf manifolds" Geometriae Dedicata. 68. 61-71 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 前田 定広: "Extrinsic shape of circles and standard imbeddings of projective spaces" Manuscripta Math.93. 267-272 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 剱持 勝衛: "On Veronese-Boruvka spheres" Archivum mathematicum. 33. 37-40 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 泉屋 周一: "Singularities of solution suefaces of gusilinear first order partial differential equations" Geometriae Dedicata. 64. 331-341 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 江尻 典雄: "Degenerate minimal surfaces of infinite total curvature in F" Kobe J.Math.14. 11-22 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 泉屋 周一: "A time-like surface in Minkowski 3-space which contains pseudo-circles" Proc.Edinburgh Math.Soc.40. 127-136 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 宮岡 礼子: "The splitting and deformations of the generalized Gauss map of compact CMC surfaces" Tohoku Math.J.(発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 足立 俊明: "Length spectrum of circles in a complex projective space" Osaka J.Math.(発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 塩浜 勝博: "The topological sphere theorem for complete submanifolds" Compositio Math.107. 221-232 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 高木 亮一: "Circular geodesic submanifolds with parallel mean curvature vector in a non-flat complex space form" Proc.Japan Acad.73. 55-57 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 荻上 紘一: "Extrinsic shape of circles and standard imbedding of a Cayley projective plane" Hokkaido Math.J.16. 411-419 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 荻上 紘一: "多様体" 共立出版, 220 (1997)

    • Related Report
      1997 Annual Research Report

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

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