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Submanifolds in Hyperbolic, Space

Research Project

Project/Area Number 09640098
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionJoetsu University of Education

Principal Investigator

MORI Hiroshi  Joetsu Univ.Edu., College Edu., Prof., 学校教育学部, 教授 (00042185)

Co-Investigator(Kenkyū-buntansha) IWASAKI Hiroshi  Joetsu Univ.Edu., College Edu., Lecturer, 学校教育学部, 講師 (80251867)
NUNOKAWA Kazuhiko  Joetsu Univ.Edu., College Edu., Lecturer, 学校教育学部, 講師 (60242468)
KUMAGAI Kohichi  Joetsu Univ.Edu., College Edu., Asso.Prof., 学校教育学部, 助教授 (80225218)
岡崎 正和  上越教育大学, 学校教育学部, 助手 (40303193)
田中 博  上越教育大学, 学校教育学部, 教授 (10033846)
中川 仁  上越教育大学, 学校教育学部, 助教授 (30183883)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1997: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordsisometric immersion / anti-de Sitter space-time / fundamental theorem for hypersurfaces / guaternionic Kahler manifold / Sasakian 3-structure / hyper Kahler structure / uometsic umumestion / anti-de Sitter Space-time / fumdamcntal thsoren for hybosinfres
Research Abstract

A fundamental problem in differential geometry is to characterize and determine all the submanifolds in a space form. A complete solution to the problem in the generality as stated above simply seems beyond the reach of the current mathematics. Historically, various conditions were imposed upon so as to make the problem somewhat more feasible, if not more viable. One of such conditions is to restrict submanifolds to being of codimension one and of the same constant curvature as the ambient space. The problem has received considerable attention under this rather restricted state ; indeed, it has seen much progress.
For example, the problem has long been settled for the Riemannian space forms of non-negative curvature, in the hyperbolic case, only some partial solutions existed until a lengthy but more complete description of the space was recently obtained, In the indefinite case, Graves gave the answer to the problem for the flat Lorentzian space forms. The case involving the de Sitter space forms was treated by Abe.
In this report, we take up the anti-de Sitter space forms of constant curvature -1. We give a. complete description of the space of the isometric immersions of H^^-_1^n into H^^-_1^<n+1>. Here we denote by H^^-_1^n the universal pseudo-Riemannian covering manifold of the n-dimensional anti-dc Sitter space-time H_1^n.

Report

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

    (22 results)

All Other

All Publications (22 results)

  • [Publications] Abe, K.and Mori, H.: "A parametsigation of isometric immersions between hyperblic space" Geom. Dedicata. 65. 31-47 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Abe, K.and Mori, H.: "A parametrization of isometric immosions between antis-de Sitter space-time" Kodai Math. J.20. 218-232 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Watanabe, Y and Mori, H.: "From Sankian 3-stuolimers to graternionic geomatsy" Arch. Math.(Bsoro). 34. 379-386 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 熊谷光一: "小学5年生の算数の授業における正当化の過程に関する研究" 日本数学教育学論究. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Nunokawa, K: "Physical modelo in mothemstical psoblam siboing" Int.J.Math.Educ.Soi.Technol.28. 877-882 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Nunokawa, K.: "Giveing new ponees to the existing elemants" J.Math.Behavior. 16. 365-378 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 岩崎浩: "具体的教材の陶冶価値を検討する意味" 株式会社大学教育出版, 214 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 熊谷光一: "共有の観点からの算数・数学の授業への接近" 産業図書株式会社, 332 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Abe, K., Mori, H.and Takahashi, H.: "A parametrization of isometric immersions between hyperbolic spaces" Geom.Dedicata. vol.65. 31-47 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Abe, K.and Mori, H.: "A parametrization of isometric immersions between anti-de Sitter space-times" Kodai Math, J.vol.20. 218-232 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Watanabe, Y.and Mori, H.: "From Sasakian 3-structures to quaternionic geometry" Arch.Math. (Brno). vol.34. 379-386 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kumagai, K.: "The Justification Process in a Fifth Grade Mathematics Classroom : From a Social Interactionist Perspective (in Japanese)" Sugaku Ronkyu. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Nunokawa, K.: "Physical models in mathematical problem solving" Int.J.Math.Educ.Sci.Technol.vol.28. 871-882 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Nunokawa, K.: "Giving new senses to the existing elements" J.Math, Behavior. vol.16. 365-378 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kumagai, K.: "Approaches to Whole-Class Lesson in Mathematics, (in Japanese)" Sangyo Tosyo. 48-60

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Watanabe,Y.and Mori,H.: "Feon Sasakiam 3-structured to guaternionie geonetry" Archivum mathemctcum. 34. 379-386 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 熊谷光一: "小学校5年生の算数の授業における正当化の過程に関する研究" 日本数学教育学会論究. to rppear.

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Abe and H.Mori: "A parametribations of isometsic immersions betueen anti-de Sitter Space-times" Kodai Mathematical J.20・3. 218-232 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Nunokawa: "Physical Modals in mathematical prblem soluring" international J.of mathimalicsl sdiealion in soienec and technslogy. Vol.28 No.6. 871-882 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Nunokawa: "guiring its senses to the existing element" J.of Matk matical Beharior. (to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] 岩崎浩: "一般教科教育学序説-具体的教材の陶治価値を検討する 意味pp54-76" 一般教科教育学研究会(近日発表予定), 214

    • Related Report
      1997 Annual Research Report
  • [Publications] 熊谷光一: "共有の観点からの算数・数学の授業への接近 pp48-60" 杉山吉茂, 332 (1997)

    • Related Report
      1997 Annual Research Report

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

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