Curvature and Symmetry (B01)

曲率和对称性（B01）

• 批准号: 444016630
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/444016630?language=en
• 关键词: Curvature; Symmetry; B01

The question of how far geometric properties of a manifold determine its global topology is a classical problem in global differential geometry. In a first subproject we study the topology of positively curved manifolds with torus symmetry. We think that the methods used in this subproject can also be used to attack the Salamon conjecture for positive quaternionic Kähler manifolds. In a third subproject we study fundamental groups of non-negatively curved manifolds. Two other subprojects are concerned with the classification of manifolds all of whose geodesics are closed and the existence of closed geodesics on Riemannian orbifolds.

流形的几何性质在多大程度上决定其整体拓扑是整体微分几何中的一个经典问题。在第一个子项目中，我们研究了具有环面对称的正曲流形的拓扑。我们认为在这个子项目中使用的方法也可以用来攻击Salamon猜想的正四元数Kähler流形。在第三个子项目中，我们研究非负弯曲流形的基本群。其他两个子项目涉及的分类流形的所有测地线是封闭的和存在的封闭测地线的黎曼orbifolds。