Ricci Flow On Locally Homogeneous Closed 4-manifolds
Communications In Analysis And Geometry
Mathematics and Computer Science
We discuss the Ricci flow on homogeneous 4-manifolds. After classifying these manifolds, we note that there are families of initial metrics such that we can diagonalize them and the Ricci flow preserves the diagonalization. We analyze the long time behavior of these families. We find that if a solution exists for all time, then the flow exhibits a type III singularity in the sense of Hamilton.
Isenberg, James, Martin Jackson, and Peng Lu. 2006. "Ricci flow on locally homogeneous closed 4-manifolds." Communications In Analysis And Geometry 14(2): 345-386.