Manifolds with Nonnegative and Almost Nonnegative Curvature

具有非负和几乎非负曲率的流形

• 批准号: 43147860
• 负责人: Professor Dr. Wilderich Tuschmann
• 金额: --
• 依托单位: Arbeitsgruppe für Differentialgeometrie
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/43147860?language=en
• 关键词: Manifolds; Nonnegative; Almost; Curvature

Global Riemannian geometry concentrates on a general understanding of the interactions between local and global properties of curved spaces, and manifolds with almost nonnegative curvature have here turned out to play a crucial role in investigating the interplay of lower curvature bounds and global shape through geometric limiting processes and collapsing techniques. The present research project aims at establishing new topological obstructions to the existence of almost nonnegatively and nonnegatively curved metrics on closed manifolds and finding further geometrical properties of these spaces.

整体黎曼几何集中在弯曲空间的局部和整体性质之间的相互作用的一般理解，和几乎非负曲率的流形在这里已经变成了在调查的相互作用的曲率下限和全球形状通过几何极限过程和崩溃技术发挥了至关重要的作用。本研究项目的目的是建立新的拓扑障碍，存在几乎非负和非负的闭流形上的弯曲度量和发现这些空间的进一步的几何性质。