Positive Ricci Soliton With A Number Of Related Issues

In this paper,we give an introduction of Ricci soliton,which is the limit solution of an important geometric partial differential equation Ricci flow established by Hamilton in geometric analysis.It describes a geometric quantity " metric " of a maniflod.This papper is divided into two parts.The first part contains chapter one to chapter five,which presents some known results of Ricci flow;the second part contains chapter six and chapter seven,in which we prove two results about Ricci soliton:1.Ricci solitons do not exist on Hopf surfaces;2.The potential function of the complete,rotationally symmetric,steady gradient K(a|¨)hler-Ricci soliton on C~n is linear with respect to the distance function.