可微分多様体の大域的構造について

可微流形的全局结构

• 批准号: 63302003
• 负责人: SHIOHAMA Katsuhiro
• 金额: $ 10.18万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63302003/
• 关键词: manifold; 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

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".

按照我们原来的计划，这个项目组织了两次大型研讨会。第35届几何研讨会在信州大学举行。 1988 年 7 月 25 日至 30 日，有 255 名参与者。上午的会议有 8 个调查讲座，下午的平行会议有 64 个一小时的讲座。研讨会上公布的大部分成果均发表于《Advanced Studies in Pure Mathematics》（《纯数学高级研究》，第 1 卷）。 18（Kinokuniya，1989），题为“微分几何和解析几何的最新主题”，摘自《数学透视》，卷。 8（学术出版社，1990）题为“流形几何”。第36届几何研讨会在东北大学举行。 1989 年 8 月 21 日至 26 日，共有 288 名参与者。上午会议有十二场调查讲座，六十八场一小时的演讲分为八场平行的下午会议。主要结果将发表于《纯数学高级研究》，第 1 卷。 22（纪伊国屋，1991），题为“微分几何的最新发展”。

项目成果

K. Shiohama: "A new version of differentiable sphere theorem. (with Y. Otsu, T. Yamaguchi)" Invent. Math.Vol. 98. 219-228 (1989)

K. Shioham：“可微球定理的新版本。（与 Y. Otsu、T. Yamaguchi 合作）”发明。

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

Takao Yamaguchi：“在曲率下界下的塌缩和挤压”Ann.of Math。

砂田利一: to appear.

砂田利一：出现。

R. Takagi: "Real hypersurfaces in Pn(C) with constant principal curvatures."

R. Takagi：“具有恒定主曲率的 Pn(C) 中的真实超曲面。”

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)

Katsue Tsurugimochi：“保留平均曲率的〓^3 平面等距变形的几何特征”Anasis de Academy Brasileira de Ciencias 61. 383-387 (1989)。