论文标题
同质Ricci流的古老解决方案在国旗歧管上流动
Ancient solutions of the homogeneous Ricci flow on flag manifolds
论文作者
论文摘要
对于任何紧凑的简单谎言组$ g $的任何国旗歧管$ m = g/k $，我们描述了均质无均衡的RICCI流的非挑剔的古代不变解决方案。这种解决方案来自$ m $不变的爱因斯坦公制，通过[böls17]，它们必须在灭绝有限的时间以及过去发展出I型奇异性。为了说明情况，我们参与了对任何标志歧管上的不正常的RICCI流动引起的动力系统的研究，其中第二个betti number $ b_ {2}（m）= 1 $，用于通用初始不变的度量。我们描述了相应的动态系统和目前的非collapsecting古代解决方案，其$α$ limit集由$ {\ Mathscr {m}}}^g $的固定点组成。基于Poincaré紧凑型方法，我们表明这些固定点对应于不变的爱因斯坦指标，我们研究了它们的稳定性，从而照亮了系统相位空间的结构。
For any flag manifold $M=G/K$ of a compact simple Lie group $G$ we describe non-collapsing ancient invariant solutions of the homogeneous unnormalized Ricci flow. Such solutions emerge from an invariant Einstein metric on $M$, and by [BöLS17] they must develop a Type I 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 $b_{2}(M)=1$, for a generic initial invariant metric. We describe the corresponding dynamical systems and present non-collapsed ancient solutions, whose $α$-limit set consists of fixed points at infinity of ${\mathscr{M}}^G$. Based on the Poincaré 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.
