Title

Ricci Flow On Locally Homogeneous Closed 4-manifolds

Document Type

Article

Publication Date

3-1-2006

Publication Title

Communications In Analysis And Geometry

Department

Mathematics and Computer Science

Abstract

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.

Volume

14

Issue

2

pp.

345-386

ISSN

1019-8385

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