Mathematical Sciences: Twistor Theory with Applications to Restricted Holonomy Geometries and Other Problems in Differential Geometry

拟议的研究需要研究流形与 限制完整性的仿射联络和 某些类的黎曼对称空间的子流形。 在后一种情况下，将特别注意表面 在四元数Kaehler流形中，这样的曲面可以 通过复分析方法研究相对于相关的 复流形 这项研究还需要研究 四维流形上的爱因斯坦度量的变形

The proposed research entails a study of manifolds with affine connections of restricted holonomy and the geometry of submanifolds of certain classes of Riemanian symmetric spaces. Particular attention in the latter case will be paid to surfaces in quaternionic-Kaehler manifolds where such surfaces can be studied by complex-analytic means relative to an associated complex manifold. This research also entails a study of deformations of Einstein metrics on 4-manifolds.