Publication details
Ancient solutions of the homogeneous Ricci flow on flag manifolds
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | Extracta Mathematicae |
| Citation | |
| Web | https://doi.org/10.17398/2605-5686.36.1.99 |
| Doi | http://dx.doi.org/10.17398/2605-5686.36.1.99 |
| Keywords | Ancient solutions; Flag manifolds; Homogeneous spacers; Ricci flow; Scalar curvature |
| Description | For any flag manifold M - G/K of a compact simple Lie group G we describe non-collapsing ancient invariant solutions of the homogeneous unnonnalized Ricci flow. Such solutions emerge from an invariant Einstein metric on M, and by [13] they must develop a Type 1 singularity in their extinction finite time, and also to the past. To illustrate the situation we engage ourselves with the global study of the dynamical system induced by the unnormalized Ricci flow on any flag manifold M - G/K with second Betti number b2(M) - 1, for a generic initial invariant metric. We describe the corresponding dynamical systems and present non-collapsed ancient solutions, whose ex-limit sot consists of fixed points at infinity of MG. Based on the Poincaro compactification method, we show that these fixed points correspond to invariant Einstein metrics and we study their stability properties, illuminating thus the structure of the system's phase space. |