Geometric structure on geometric manifolds which admit Lie group transformations and various Rigidity

几何流形上的几何结构，允许李群变换和各种刚性

• 批准号: 20340013
• 负责人: KAMISHIMA Yoshinobu
• 金额: $ 3.91万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20340013/
• 关键词: 幾何学; 微分幾何学; 微分トポロジー; 可解等質空間; Seifertファイバー空間; 可微分剛性; Fefferman; Lorentz構造; Parabolic構造; 因果性; 変換群; Vague conjecture; Conformal structure; Rigidity; LcK structure; Kaehler structure; Homogeneous manifold; Sasaki manifold; Fefferman-Lorentz

We have examined the following projects.(1) Approach from geometry and topology concerning conformally Fefferman-Lorentz manifolds.(1) We proved the analogue of the Obata-Ferrand theorem to Lorentz manifolds.(2) We proved the Kuiper's problem that if the developing map is not surjective on the universal cover of S^<n-1,1>, then it is a covering map onto its image under the existence of causal vector fields.(2) We studied the infrasolv-fiber space structure and the smooth rigidity on the closed aspherical manifolds of the mixed type. As an application, we proved the smooth rigidity of compact aspherical homogeneous manifolds.

(1)从几何和拓扑学的角度研究共形Fefferman-Lorentz流形.(1)证明了Obata-Ferrand定理类似于Lorentz流形.(2)证明了Kuiper问题：如果发展映射在S^&lt；n-1，1&gt；的泛覆盖上不是满射的，那么在因果向量场的存在下它是像上的覆盖映射.(2)研究了混合型闭非球面上的次纤维空间结构和光滑刚性.作为应用，我们证明了紧致非球面齐次流形的光滑刚性。

项目成果

Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies

立方同宿切线的持续反单调分岔和奇异吸引子

• 发表时间: 2008
• 期刊: Nonlinearity 21
• 作者: S. Kiriki;T. Soma
• 通讯作者: T. Soma

Energy of knots and the infinitesimal cross ratio, Proceedings of the Conference Groups

结的能量和无穷小的交比，会议小组论文集

• 发表时间: 2008
• 期刊: Homotopy and Configuration Spaces, Geometry and Topology Monographs Vol.13
• 作者: M.Ando;T.Suzuki;H-F.Yamada;Hidehiko Kamiya;T. Ashikaga;今井淳
• 通讯作者: 今井淳

Pseudoharmonic maps and vector fields on CR manifolds

CR 流形上的伪调和映射和矢量场

• 发表时间: 2010
• 期刊: Jour.Math.Soc.Japan Vol.62
• 作者: 神島芳宣;Sorin Dragomir
• 通讯作者: Sorin Dragomir

Conformally flat Fefferman-Lorentz manifolds

共形平坦费弗曼-洛伦兹流形

• 发表时间: 2010
• 作者: 内野智之;高橋智;Tomoyuki Arakawa;Ichiro Shimada;神島芳宣
• 通讯作者: 神島芳宣

Cohomological rigidity of real Bott manifolds

• DOI: 10.2140/agt.2009.9.2479
• 发表时间: 2008-07
• 期刊: arXiv: Algebraic Topology
• 作者: Y. Kamishima;M. Masuda