Communications in Analysis and Geometry

Volume 14 (2006)

Number 2

Ricci flow on locally homogeneous closed 4-manifolds

Pages: 345 – 386

DOI: http://dx.doi.org/10.4310/CAG.2006.v14.n2.a5

Authors

James Isenberg

Martin Jackson

Peng Lu

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.

2010 Mathematics Subject Classification

53C44

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