1990 Fiscal Year Annual Research Report

可微分多様体の大域的構造について

Research Project

Project/Area Number	63302003
Research Institution	Kyushu University
Principal Investigator	塩浜勝博九州大学, 理学部, 教授 (20016059)
Co-Investigator(Kenkyū-buntansha)	酒井隆岡山大学, 理学部, 教授 (70005809) 荻上紘一東京都立大学, 理学部, 教授 (10087025) 高木亮一千葉大学, 理学部, 教授 (00015562) 砂田利一名古屋大学, 理学部, 教授 (20022741) 落合卓四郎東京大学, 理学部, 教授 (90028241)
Keywords	多様体 / アインシュタイン計量 / 曲率 / ヤングミルズ接続 / 等質空間 / 極小曲面 / リ-接触構造 / ラプラシアン
Research Abstract	当初の計画に従い、アメリカ数学会のサマ-インティテュ-ト方式による分科会形式の幾何学研究会を計画した。まず初年度は信州大学教養部において1988年7月25日より30日まで開催し、255名の参加者を得て8の総合講演が午前に64の1時間講演が8分科会に分かれ午後に行なわれた。ここで得られた研究成果の多くは2冊の単行本として出版されている。これらはAdvanced Studies in Pure Mathematics,Vol.18(紀伊国屋、1989年)から“Recent Topics in Analytic and Differential Geometry"及びPerspectives in Mathematics,Vol.8(Academic Press,1990年)から“Geometry of Manifolds"である。平成元年度は東北大学教養部において1989年8月21日より26日まで開催し、288名の参加者を得た。午前に8の総合講演が行なわれ、午後は8分科会に分かれて68の1時間講演が行なわれた。これらの成果のうち主なものはAdvanced Studiesin Pure Mathematics,Vol.22に“Recent Developments in Differential Geometry"として近々出版の予定である。平成2年度は国際数学者会議との関連においてPreconference in Differential Geometryを東京都立大学において開催した。世界各地からの研究者との交流を緊密に保つための意見交換を行ない、各大学において外国人研究者を迎え入れる計画をたてた。

Research Products
(23 results)

All Other

All Publications (23 results)

[Publications] 深谷賢治: "Collapsing Riemannian manifolds to ones of lower dimension II" J.Math.Soc.Japan. 41. 333-356 (1989)
[Publications] 二木昭人: "A Lie algebra character and Ka^^¨hlerーEinstein metrics" Proc.Symp.Pure Math.,.
[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)
[Publications] 佐々木武: "Linear differential equations modeled after hyperquadrics" Tohoku Math.J.,. 41. 321-348 (1989)
[Publications] 塩浜勝博: "Recent Developments in Sphere Theorems" Proc.Symp.Pure Math.(AMS).
[Publications] 勝田篤: "Closed orbits in homology classes(砂田利一と共著)" IHES.Publ.71. (1990)
[Publications] 山口孝男: "Collapsing and pinching under a lower curvature bound" Ann.of Math.
[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)
[Publications] 印南信宏: "Manifolds without conjugate points and with integral curvature zero" J.Math.,Soc.Japan.41. 251-261 (1989)
[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)
[Publications] 小林亮一: "Ricciーflat Ka^^¨hler metrics on affine algebraic manifolds II" Math.Ann.,. 287. 175-180 (1990)
[Publications] 酒井隆: "On levels of the distance function from the boundary of convex domain"
[Publications] 高木亮一: "Real hypersurfaces in pn(С) with constant principal curvatures"
[Publications] 丹野修吉: "Variational problems on contact Riemannian manifolds" Trans.Amer.Math.Soc.,. 314. 349-379 (1989)
[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)
[Publications] 砂田利一: "Periodic Schroedinger operators on a manifold(小野薫と共著)" Forum Math.,. 1. 69-79 (1989)
[Publications] 坂根由昌: "Nonーhomogeneous Ka^^¨hlerーEinstein metrics on compact complex manifolds" Osaka J.Math.,. 25. 939-959 (1988)
[Publications] 砂田利一: "A periodic Schroedinger operator on an abel cover"
[Publications] 竹内勝: "Two numbers of symmetric Rーspaces" Nagoya J.Math.,. 115. 43-46 (1989)
[Publications] 浦川肇: "Spectra of Riemannian manifolds without focal points" Geometry of Manifolds,Perspectuves in Math.,. 8. 435-444 (1989)
[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)
[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)
[Publications] 塩浜勝博(編): "Geometry of Manifolds,Perspectives in Mathematics,Vol.8." Academic Press, 517 (1990)

1990 Fiscal Year Annual Research Report

可微分多様体の大域的構造について

Principal Investigator

塩浜 勝博 九州大学, 理学部, 教授 (20016059)

Research Products

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

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

[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)

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

[Publications] 塩浜 勝博: "Recent Developments in Sphere Theorems" Proc.Symp.Pure Math.(AMS).

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

[Publications] 山口 孝男: "Collapsing and pinching under a lower curvature bound" Ann.of Math.

[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)

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

[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)

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

[Publications] 酒井 隆: "On levels of the distance function from the boundary of convex domain"

[Publications] 高木 亮一: "Real hypersurfaces in pn(С) with constant principal curvatures"

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

[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)

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

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

[Publications] 砂田 利一: "A periodic Schroedinger operator on an abel cover"

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

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

[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)

[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)

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

塩浜勝博九州大学, 理学部, 教授 (20016059)

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

[Publications] 二木昭人: "A Lie algebra character and Ka^^¨hlerーEinstein metrics" Proc.Symp.Pure Math.,.

[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)

[Publications] 佐々木武: "Linear differential equations modeled after hyperquadrics" Tohoku Math.J.,. 41. 321-348 (1989)

[Publications] 塩浜勝博: "Recent Developments in Sphere Theorems" Proc.Symp.Pure Math.(AMS).

[Publications] 勝田篤: "Closed orbits in homology classes(砂田利一と共著)" IHES.Publ.71. (1990)

[Publications] 山口孝男: "Collapsing and pinching under a lower curvature bound" Ann.of Math.

[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)

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

[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)

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

[Publications] 酒井隆: "On levels of the distance function from the boundary of convex domain"

[Publications] 高木亮一: "Real hypersurfaces in pn(С) with constant principal curvatures"

[Publications] 丹野修吉: "Variational problems on contact Riemannian manifolds" Trans.Amer.Math.Soc.,. 314. 349-379 (1989)

[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)

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

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

[Publications] 砂田利一: "A periodic Schroedinger operator on an abel cover"

[Publications] 竹内勝: "Two numbers of symmetric Rーspaces" Nagoya J.Math.,. 115. 43-46 (1989)

[Publications] 浦川肇: "Spectra of Riemannian manifolds without focal points" Geometry of Manifolds,Perspectuves in Math.,. 8. 435-444 (1989)

[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)

[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)

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