Quasi-convergence of model geometries under the Ricci flow
Let \(g\) and \(h\) be evolving Riemannian metrics on a manifold \(M^n\). In an earlier paper, Knopf formulated the notion of quasi-convergence of \(g\) to \(h\) if for any \(\varepsilon >0\) there exists a time \(t_{\varepsilon}\) such that \(\sup_{M^n \times [t_{\varepsilon}, \infty)} |g-h|_h < \varepsilon\). This is actually an equivalence relation which can be used to classify the asymptotic behavior of Ricci flows which exist for all time. The present paper focuses on the study of quasi-convergence equivalence classes of locally homogeneous metrics for which the Ricci flow exists to infinity. The authors consider the most general families of such metrics by using model geometries \((\chi, \mathcal{G})\), with \(\mathcal{G}\) minimal.
scientific article; zbMATH DE number 1833142