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可微分多様体の大域的構造について

Research Project

Project/Area Number 63302003
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionKyushu University

Principal Investigator

SHIOHAMA Katsuhiro  Kyushu Univ. Fac. of Sci. Professor, 理学部, 教授 (20016059)

Co-Investigator(Kenkyū-buntansha) SAKAI Takashi  Okayama Univ. Fac. of Sci. Professor, 理学部, 教授 (70005809)
OGIUE Kouichi  Tokyo Metropolitan Univ. Fac. of Sci. Professor, 理学部, 教授 (10087025)
TAKAGI Ryoichi  Chiba Univ. Fac. of Sci. Professor, 理学部, 教授 (00015562)
SUNADA Toshikazu  Nagoya Univ. Fac. of Sci. Professor, 理学部, 教授 (20022741)
OCHIAI Takushiro  Tokyo Univ. Fac. of Sci. Professor, 理学部, 教授 (90028241)
浦川 肇  東北大学, 教養部, 助教授 (50022679)
Project Period (FY) 1988 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥15,900,000 (Direct Cost: ¥15,900,000)
Fiscal Year 1990: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1989: ¥7,100,000 (Direct Cost: ¥7,100,000)
Fiscal Year 1988: ¥5,800,000 (Direct Cost: ¥5,800,000)
Keywordsmanifold / Einstein metric / curvature / Yang-Mills connection / homogeneous spaces / minimal surfaces / Lie contact structure / Laplacian / リ-接触構造 / 複素多様体 / 力学系 / 調和写像 / 熱方程式 / リッテ曲率 / リ-マン多様体 / リーマン多様体 / 対称空間 / ラプラスベルトラミ作用素 / 部分多様体
Research Abstract

According to our original plan, two large-scale symposiums were organized by this project.
The 35th symposium on Geometry was held at Shinshu Univ. From 25-30, July 1988 with 255 participants. There were eight survey lectures in the morning sessions and sixty-four one-hour-talks divided in to mine parallel afternoon sessions. Most of the results announced in the symposium have been published from Advanced Studies in Pure Mathematics, Vol. 18 (Kinokuniya, 1989) entitled "Recent Topics in Differential and Analytic Geometry" and from Perspectives in Mathematics, Vol. 8 (Academic Press, 1990) entitled "Geometry of Manifolds".
The 36th symposium on Geometry was held at Tohoku Univ. From 21-26 August 1989 with 288 participants. There were twelve survey lectures in morning sessions and sixty-eight one-hour-talks divided into eight parallel afternoon sessions. The main results will have been published from Advanced Studies in Pure Mathematics, Vol. 22 (Kinokuniya, 1991) entitled "Recent Developments in Differential Geometry".

Report

(4 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • 1988 Annual Research Report
  • Research Products

    (85 results)

All Other

All Publications (85 results)

  • [Publications] 深谷 賢治: "Collapsing Riemnnian manifold to ones of lower dimension II" J.Math.Soc.Japan. 41. 333-356 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 二木 昭人: "A Lie algebra character and Kahler ーEinstein metrics" Proc.Symp.Pure Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 金井 雅彦: "Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations" Ergod.Theory and Dynam.Systems.,. 8. 215-239 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 佐々木 武: "Linear differential equations modeled after hyperquadrics" Tohoku Math.J.,. 41. 321-348 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 塩浜 勝博: "Recent Development in Sphere Theorems" Proc.Symp.Pure Math.(AMS).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 勝田 篤(砂田 利一と共著): "Closed orbits in homology classes" IHES.Publ.71. (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 山口 孝男: "Collapsing and pinching under a lower curvature bound" Ann.of Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 加須栄 篤: "On a construction of coordinates at infinity on manifolds with fast curvature decay(板東 重稔、中島 啓と共著)" Invent.Math.97. 313-349 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 印南 信宏: "Manifolds without conjugate points and with integral curvature zero" J.Math.,Soc.Japan.41. 251-261 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 剱持 勝衛: "A geometric characterization of an isometric deformation of flat surfaces in 〓^3 preserving mean curvatures" Anasis de Academic Brasileira de Ciencias. 61. 383-387 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 小林 亮一: "Ricciーflat Kahler metrics on affine algebraic manifolds 2" Math.Ann.,. 287. 175-180 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 酒井 隆: "On levels of the distance function from the boundary of convex domain"

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 高木 亮一: "Real hypersurfaces in Pn(〓) with constant principal curvatures"

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 丹野 修吉: "Variational problems on contact Riemannian manifolds" Trans.Amers.Math.Soc.,. 314. 349-379 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 塩浜 勝博(大津 幸男,山口 孝男と共著): "A new version of differentiable sphere theorem" Invent.Math.,. 98. 219-228 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 砂田 利一(小野 薫と共著): "Periodic Schroedinger operators on a manifold" Forum Math.,. 1. 69-79 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 坂根 由昌: "Nonーhomogeneous Ka^¨hlerーEinstein metrics on compact complex manifolds" Osaka J.Math.,. 25. 939-959 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 砂田 利一: "A periodic Schroedinger operator on an abel cover"

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 竹内 勝: "Two numbers of symmetric Rーspaces" Nagoya J. Math.,. 115. 43-46 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 浦川 肇: "Spectra of Riemannian manifolds without focal points" Geometry of Manifolds,Perspectuves in Math.,. 8. 435-444 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 森本 徹: "Theoreme de CartanーKa^¨hler dans une classe de fonctions formelles Gevrey" C.R.Acad. Sci. Paris. 311. 433-436 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 落合 卓四郎 (編): "Recent Topics in Differential and Analytic Geometry,Adv.Stud.Pure Math.Vol.18" 紀伊国屋ーAcademic Press, (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 塩浜 勝博 (編): "Gemetry of Manifolds,Perspective in Mathematics,Vol.8." Academic Press, 517 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. FUKAYA: "Collepsing Riemannian manifolds to ones of lower dimension II." J. Math. Soc. Japan. Vol. 41. 333-356 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] A. Niki: "A Lie algebra character and kahler-Einstein metrics." Proc. Symp. Pure Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] M. Kanai: "Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations." Ergod. Theory and Dynam. Symstems. Vol. 8. 215-239 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T. Sasaki: "Linear differential equations modeled after hyperquadrics." Tohoku Math. J.Vol. 41. 321-348 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Shiohama: "Recent Developments in Sphere Theoreme." Proc. Symp. Pure Math. (AMS).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] A. Katsuda: "Closed orbits in homology classes. (with T. Sunada)" IHES. Publ.No. 71. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T. Yamaguchi: "Collapsing and pinching under a lower curvature bound." Ann. of Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] A. Kasue: "On a construction of coordinates at infinity on manifolds with fast curvature decay. (with S. Bando, H. Nakashima)" Invent. Math.Vol. 97. 313-349 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] N. Innami: "Manifolds without conjugate points and with integral curvature zero." J. Math. Soc. Japan.Vol. 41. 251-261 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Kennmotsu: "A geometric characterization of an isometric deformation of flat surfaces in R^3 preserving mean curvatures." Anais de Academia Brasileirade Ciencias. Vol. 61. 383-387 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] R. Kobayashi: "Ricci-flat Kahler metrics on affine algebraic manifolds II." Math. Ann.Vol. 287. 175-180 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T. Sakai: "On livels of the distance function from the boundary of convex domain."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] R. Takagi: "Real hypersurfaces in Pn(C) with constant principal curvatures."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] S. Tanno: "Variational problems on contact Riemannian manifolds." Trans. Amer. Math. Soc.Vol. 314. 349-379 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Shiohama: "A new version of differentiable sphere theorem. (with Y. Otsu, T. Yamaguchi)" Invent. Math.Vol. 98. 219-228 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T. Sunada: "Periodic Schroedinger operators on a manifold. (with k. Ono)" Forum Math.Vol. 1. 69-79 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Y. Sakane: "Non-homogeneous Kahler-Einstein metrics on compact complex manifolds. (with N. Koiso)" Osaka J. Math.Vol. 25. 939-959 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T. Sunada: "A periodic Schroedinger operator on an abel cover."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] M. Takeuchi: "Two numbers of symmetric R-spaces." Nagoya J. Math.Vol. 115. 43-46 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] H. Urakawa: "Spectra of Riemannian manifolds without focal points." Geometry of Manifolds Perspectives in Math.Vol. 8. 435-444 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T. Morimoto: "Theoreme de Cartan-Kahler dans une classe de fonctions formelles Gevrey." C. R. Acad. Sci. Paris. Vol. 311. 433-436 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] T. Ochiai (editor): Kinokuniya-Academic Press.Recent Topics in Differential and Analytic Geometry, Adv. Stud. Pure Math. Vol. 18, 1990

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Shiohama (editor): Geometry of Manifolds, Perspectives in Mathematics, Vol. 8, 517 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 深谷 賢治: "Collapsing Riemannian manifolds to ones of lower dimension II" J.Math.Soc.Japan. 41. 333-356 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 二木 昭人: "A Lie algebra character and Ka^^¨hlerーEinstein metrics" Proc.Symp.Pure Math.,.

    • Related Report
      1990 Annual Research Report
  • [Publications] 金井 雅彦: "Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations" Ergod.Theory and Dynam.Systems.,. 8. 215-239 (1988)

    • Related Report
      1990 Annual Research Report
  • [Publications] 佐々木 武: "Linear differential equations modeled after hyperquadrics" Tohoku Math.J.,. 41. 321-348 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 塩浜 勝博: "Recent Developments in Sphere Theorems" Proc.Symp.Pure Math.(AMS).

    • Related Report
      1990 Annual Research Report
  • [Publications] 勝田 篤: "Closed orbits in homology classes(砂田利一と共著)" IHES.Publ.71. (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 山口 孝男: "Collapsing and pinching under a lower curvature bound" Ann.of Math.

    • Related Report
      1990 Annual Research Report
  • [Publications] 加須栄 篤: "On a construction of coordinates at infinity on manifolds with fast curvature decay(板東重稔,中島啓と共著)" Invent.Math.97. 313-349 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 印南 信宏: "Manifolds without conjugate points and with integral curvature zero" J.Math.,Soc.Japan.41. 251-261 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 剱持 勝衛: "A geometric characterization of an isometric deformation of flat surfaces in IR^3 preserving mean curvatures" Anais de Academia Brasileira de Cie^<^>ncias. 61. 383-387 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 小林 亮一: "Ricciーflat Ka^^¨hler metrics on affine algebraic manifolds II" Math.Ann.,. 287. 175-180 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 酒井 隆: "On levels of the distance function from the boundary of convex domain"

    • Related Report
      1990 Annual Research Report
  • [Publications] 高木 亮一: "Real hypersurfaces in pn(С) with constant principal curvatures"

    • Related Report
      1990 Annual Research Report
  • [Publications] 丹野 修吉: "Variational problems on contact Riemannian manifolds" Trans.Amer.Math.Soc.,. 314. 349-379 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 塩浜 勝博: "A new version of differentiable sphere theorem(大津幸男,山口孝男と共著)" Invent.Math.,. 98. 219-228 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 砂田 利一: "Periodic Schroedinger operators on a manifold(小野薫と共著)" Forum Math.,. 1. 69-79 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 坂根 由昌: "Nonーhomogeneous Ka^^¨hlerーEinstein metrics on compact complex manifolds" Osaka J.Math.,. 25. 939-959 (1988)

    • Related Report
      1990 Annual Research Report
  • [Publications] 砂田 利一: "A periodic Schroedinger operator on an abel cover"

    • Related Report
      1990 Annual Research Report
  • [Publications] 竹内 勝: "Two numbers of symmetric Rーspaces" Nagoya J.Math.,. 115. 43-46 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 浦川 肇: "Spectra of Riemannian manifolds without focal points" Geometry of Manifolds,Perspectuves in Math.,. 8. 435-444 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] 森本 徹: "Theoreme de CartanーKa^^¨hler dans une classe de fonctions formelles Gevrey" C.R.Acad.Sci.Paris. 311. 433-436 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 落合 卓四郎(編): "Recent Topics in Differential and Analytic Geometry,Adv.Stud.Pure Math.Vol.18" 紀伊国屋ーAcademic Press, (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 塩浜 勝博(編): "Geometry of Manifolds,Perspectives in Mathematics,Vol.8." Academic Press, 517 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 塩濱勝博: "Locally Convex Sets in Nonnegatively Curved Manifolds" Preptint.

    • Related Report
      1989 Annual Research Report
  • [Publications] 砂田利一: "Homology of closed orbits(with A.Katsuda)" to appear in I.H.E.S.Publ.(1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 佐々木武: "On a theorem of Chern and Terng on affine surfaces(with K.Nomizu)" to appear in Manuscripta Math.

    • Related Report
      1989 Annual Research Report
  • [Publications] 浦川肇: "Classification of harmonic mappings of constant energy density into spheres(with J.S.Park)" Preprint.

    • Related Report
      1989 Annual Research Report
  • [Publications] 剣持勝衛: "Isometric deformation of surfaces in R^3 preserving the mean curvature function(with A.G.Colares)" Pacific Journal of Math.136. 71-80 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 満渕俊樹: "Einstein Kahler metrics with positive Ricci curvature(with A.Futaki and Y.Sakane)" Recent Topics in Differential Geometry(Advanced Studies in Pure Mathematics,vol.18). 18. (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 塩濱勝博(編集): "Geometry of Manifolds(Prespectives in Math.Vol.8)" HBT-Academic Press, 517 (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 落合卓四郎(編集): "Recent Topics in Differential Geometry" 紀国屋書店, 500 (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 塩浜勝博: Invent.Math.

    • Related Report
      1988 Annual Research Report
  • [Publications] 竹内勝: Osaka J.Math.25. 259-297 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 佐々木武: Mathematische Annalen. 282. 69-93 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 砂田利一: to appear.

    • Related Report
      1988 Annual Research Report
  • [Publications] 深谷賢治: J.Differential Geometry. 28. 1-21 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 伊藤光弘: Kodai Math.J.11. 334-360 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] 塩浜勝博 編: "Geometry of Manifolds" Academic Press, 580 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] 落合卓四郎 編: "Einstein Metrics" 紀国屋書店, 300 (1989)

    • Related Report
      1988 Annual Research Report

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Published: 1988-04-01   Modified: 2016-04-21  

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