Spaces with sectional and Ricci curvature bounds

具有截面和里奇曲率边界的空间

• 批准号: 342868-2012
• 负责人: Kapovitch, Vitali
• 金额: $ 1.82万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=572509
• 关键词: Spaces; sectional; Ricci; curvature; bounds

The proposal concerns the study of metric spaces with various curvature bounds. A positive lower curvature bound means that locally a space looks like a hill. Negative curvature means that it locally looks like a saddle. In particular the proposal will address what effects such local bounds can have on global topological shape of the space such as the number of holes of various dimensions a space might have.

该建议涉及研究度量空间与各种曲率的界限。正的下曲率界意味着局部空间看起来像一座山。负曲率意味着它局部看起来像一个马鞍。特别是，该建议将解决这种局部边界对空间的全局拓扑形状的影响，例如空间可能具有的各种维度的孔的数量。