Manifolds with reduced holonomy.

拟议研究的主题领域是微分几何和全球分析。完整群是黎曼流形的基本不变量。近年来，人们对“特殊几何”产生了很大的兴趣，例如在Calabi-Yau，G_2和Spin（7）流形中，由于考虑到完整性约化或对曲率的限制，以及它们的“校准”极小子流形。这些结构通常可以表示为几何上自然的非线性和椭圆型偏微分方程的解。有一些重要的公开问题，一般几何和拓扑性质的后者流形，他们的变形和奇点，以及建设和分类的例子。博士项目将处理由这些开放性问题中的一些激发的研究任务。

The subject area of proposed research is differential geometry and global analysis. The holonomy group is a fundamental invariant of a Riemannian manifold. In recent years, there has been much interest in `special geometries' arising e.g. in Calabi--Yau, G_2 and Spin(7) manifolds from considerations of holonomy reduction or restrictions on the curvature and also their `calibrated' minimal submanifolds. These structures may often be expressed as solutions of geometrically natural non-linear and elliptic partial differential equations. There is a number of important open questions concerning general geometric and topological properties of the latter manifolds, their deformations and singularities, as well as construction and classification of examples. The PhD project will deal with research tasks motivated by some of these open questions.