Riemannian manifolds with special holonomy

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。在现代几何中，人们对具有特殊“对称性”的空间有很多兴趣和活动。这包括简化完整的黎曼流形，特别是Calabi-Yau流形、G_2流形和Spin(7)流形以及它们的标定子流形，它们是最小曲面的推广。这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、例子的构造或分类等新的有趣问题。这个项目将处理一些新出现的问题。

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.