Riemannian manifolds with special holonomy

具有特殊完整性的黎曼流形

• 批准号: 2261110
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2261110
• 关键词: Riemannian; manifolds; special; holonomy

The subject area of this project is differential geometry. The holonomy group is a fundamental invariant of a Riemannian manifold. In modern geometry, there is much interest and activity concerning spaces having particular `symmetries'. This includes Riemannian manifolds with reduced holonomy, in particular Calabi-Yau varieties, G_2 and Spin(7) manifolds and also their calibrated submanifolds which are generalizations of minimal surfaces. One is naturally led to new interesting questions about geometrical and topological properties of the above spaces, their deformations and singularities, construction or classification of examples. The project will deal with some of the arising questions.

这个项目的主题领域是微分几何。完整群是黎曼流形的一个基本不变量。在现代几何学中，有许多关于具有特殊“对称性”的空间的兴趣和活动。这包括具有约化完整的黎曼流形，特别是Calabi-Yau簇、G_2流形和Spin(7)流形，以及它们的标定子流形，它们是极小曲面的推广。人们自然会引出关于上述空间的几何和拓扑性质、它们的变形和奇点、例子的构造或分类的新的有趣的问题。该项目将解决一些由此产生的问题。