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Research on transformation groups from the topological viewpoint

Research Project

Project/Area Number 10640058
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

UCHIDA Fuichi  Faculty of Science, Yamagata Univ. Professor, 理学部, 教授 (90028126)

Co-Investigator(Kenkyū-buntansha) ASOH Tohl  Graduate School of Information Sciences, Tohoku Univ. Associate Professor, 情報科学研究科, 助教授 (00111352)
YASUI Tsutomu  Faculty of Education, Kagoshima Univ. Professor, 教育学部, 教授 (60033891)
II Kiyotaka  Faculty of Science, Yamagata Univ. Associate Professor, 理学部, 助教授 (10007180)
内田 吉昭  山形大学, 理学部, 助教授 (80280890)
尾方 隆司  山形大学, 理学部, 教授 (10042425)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1999: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1998: ¥1,900,000 (Direct Cost: ¥1,900,000)
Keywordstransformation groups / non-compact Lie group / maximal compact subgroup / complex projective space / 非コンパリトリイ群 / 極小曲面 / 四元数射影空間 / 接バンドル / 結び目理論 / 結び目解消操作
Research Abstract

In a previous project, F. Uchida have studied smooth SOィイD20ィエD2(p,q)-actions on SィイD1p+q-1ィエD1, each of which is an extension on the standard SO(p) x SO(q) action on SィイD1p+q-1ィエD1.
In this project, as a main theme, we study smooth Sp(p,q)-action on SィイD14p+4q-1ィエD1, each of which is an extension of the standard Sp(p) x Sp(q) action on SィイD14p+4q-1ィエD1. This standard action has condimension-one principal orbits with Sp(p-1)x Sp(q-1) as the principal isotropy subgroup. Furthermore, the fixed point set of the restricted Sp(p-1) x Sp(q-1) action is diffeomorphic to the seven-sphere SィイD17ィエD1.
We can show such SOィイD20ィエD2(p,q)-action on SィイD1p+q-1ィエD1 is characterized by a pair (φ,∫) satisfying certain conditions, whereφ is a smooth Sp(1,1)-action on SィイD17ィエD1, and ∫: SィイD17ィエD1 → PィイD21ィエD2(H) is a smooth function.
The pair(φ,∫) was introduced by T. Asoh to consider smooth SL(2,C)-actions on the 3-sphere, and was improved by F. Uchida.
As related topics, T. Yasui has a result on embeddings of n-manifolds into complex projective n-space, T. Asoh studies smooth actions of SL(2,C) on the 4-sphere, each of which is an extension of an orthogonal action of SU(2) on the 4-sphere, and K. Ii has given a method of construction and a characterization of complex structures on tangent bundles of complex projective spaces and quaternion projective spaces.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (9 results)

All Other

All Publications (9 results)

  • [Publications] 井伊清隆: "Kaehler structures on the tangent bundle of Riemannian manifolds of constant positive curvature"Bullctin of Yamagata Univ. Nat. Sei. 14-3. 141-154 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 安井孜: "Enumerating embeddings of n-manifolds into complex projective n-space"Hiroshima Math. J.. 29. 579-590 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kiyotaka Ii: "Kaehler structures on the tangent bundle of Riemannian manifolds of constant positive curvature"Bull. Yamagata Univ. Nat. Sci.. 14-3. 141-154 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Tsutomu Yasui: "Enumerating embeddings of n-manifolds into complex projective n-space"Hiroshima Math. J.. 29. 579-590 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 井伊清隆: "Kaehler structures on the tangent bundle of Riemannian manifolds of constant positive curvature"Bultction of Yamagata.Nat.Sci.. 14-3. 141-154 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 安井 孜: "Enumerating enbeddings of n-manifolds into complex projective n-space"Hiroshina Math.J. 29. 579-590 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 尾方隆司: "P^2(C)内のケーラー角度一定な極小曲面" 数理解析研究所講究録. 1069. 83-91 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 井伊清隆: "Kaehler structures on the tangeut bundle of Riemannian・・・" Bull.Yamagata Univ.Nat.Sci.14-3. 141-154 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 内田吉昭: "Delta-unkuotting number for knots" J.Knot theory and its Ramifications. 7-5. 639-650 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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