Ricci flow on locally homogeneous closed 4-manifolds

Details Ricci flow on locally homogeneous closed 4-manifolds Ricci flow on locally homogeneous closed 4-manifolds

2005-02-08

arxiv.org/abs/math/0502170v1

Mathematics

Differential Geometry

32 pages

Scientific paper

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.

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