Mathematical Sciences: On Certain Rigidity Problems in Kaehler Geometry

一个复变量的完全单值化定理 对一维单连通复流形进行了分类。 对于高维复形没有相应的结果 流形，重要的是要设法找到一些方法， 提供替代分类。主要研究者 我会尝试把那些高维的复流形 其满足收缩曲率条件。 一组对象的分类，这些对象满足一个公共 性质或条件是数学家用来理解 结构及其关系。如果一个人可以列出所有的对象 有一个有限的共同财产，那么一个更好的 理解财产和物品。校长 调查人员将尝试使用歧管或表面来进行此操作 其曲率福尔斯落在一定范围内。

The uniformization theorem of one complex variable completely classifies the one dimensional simply connected complex manifolds. There is no corresponding result for higher dimensional complex manifolds and it is important to try to find some method which will provide a substitute classification. The principal investigator will try to classify those higher dimensional complex manifolds which satisfy a pinched curvature condition. Classification of a set of objects which satisfy a common property or condition is one tool mathematicians use to understand structures and their relationships. If one can list all objects which have a restricted common property, then one better understands the property and the objects. The principal investigator will attempt to do this with manifolds or surfaces whose curvature falls between certain bounds.