在微分几何中，怎样在一定的曲率条件下去了解给定流形的拓扑一直是一个中心的课题。近三十年来，研究这个课题的一个强有力的工具就是Ricci流。随着Ricci流理论的发展，许多重要的几何问题得以解决，这也极力地推动着微分几何的蓬勃发展。运用Ricci流理论去解决几何问题的一个关键，就是得到奇点的结构，这就要求我们去分析Ricci流的奇点，其中重要的一步就是完全分类梯度Ricci soliton这一重要的奇点模型。另一方面，具有正迷向曲率的紧致黎曼流形具有丰富的几何和拓扑信息，这类流形的研究在国际上一直是一个热点问题。在本项目中，我们主要是通过Ricci流去研究这类流形，着重分析奇点的结构。我们期望能更多的了解其几何性质，包括得到重要的曲率拼挤估计，并以此为基础，完全分类对应类型的soliton。更进一步，soliton 的完全分类会帮助我们了解奇点的结构，进而得到具有正迷向曲率的流形的分类。

In differential geometry, how to understand the topology of a given manifold under certain curvature conditions is a central topic. In the past 30 years, a powerful tool to study this subject is Ricci flow. With the development of the Ricci flow theory, many important geometric problems can be solved, which also promoted the vigorous development of differential geometry. Using the Ricci flow theory to solve geometric problems, the key is to get the structure of singularities, which requires us to analyze the singularity of Ricci flow, one important step is to complete classify gradient Ricci solitons, which are the important models of singularities. On the other hand, compact Riemannian manifolds with positive isotropic curvature have a rich geometric and topology information, to study such kind of manifolds is a hot international issue. In this project, we will use Ricci flow to study such kind of manifolds, focus on analyze the structure of singularities. We look forward to learn more about the geometric properties, including some important curvature pinching estimates, then we try to complete classify the corresponding type of solitons. Furthermore, the complete classification of solitons will help us to understand the structure of the singularity well, thus the classification of manifolds with positive curvature.