Global Analysis on Riemannian Manifolds

小行星9703656 这个项目是在该地区的黎曼和卡勒几何。更具体地说，研究者是使用里奇流来研究各种问题，在黎曼和卡勒几何。例如，研究者希望证明一个具有正全纯双截曲率的完备非紧Kahler流形与复欧氏空间是双全纯的，这是该领域的一个著名问题。 黎曼流形是曲面的高维推广;卡勒流形是黎曼流形的复杂模拟。物理学家经常试图将宇宙描述为具有某些附加性质的黎曼流形或卡勒流形。里奇流背后的思想是以一种特殊的方式随着时间的推移改变给定的度量-度量定义了底层流形上的距离概念，并观察所得的度量族如何与流形的拓扑或形状属性相互作用。

9703656 Shi This project lies in the area of Riemannian and Kahler geometry. More specifically, the investigator is to use the Ricci flow to study various problems in Riemannian and Kahler geometry. For example, the investigator wishes to show that a complete noncompact Kahler manifold with positive holomorphic bisectional curvature is biholomorphic to complex Euclidean space, a well-known problem in the area. Rimannian manifolds are higher dimensional generalizations of curved surfaces; Kahler manifolds are a complex analog of Riemannian manifolds. Physicists often attempt to describe the universe as a Riemannian or Kahler manifold possessing certain additional properties. The idea behind the Ricci flow is to vary the given metric - a metric defines the notion of distance on the underlying manifold - over time in a special way and to see how the resulting family of metrics interact with the topology or shape properties of the manifold.