论文标题
在球体上的同质指标的RICCI流动上
On the Ricci Flow of Homogeneous Metrics on Spheres
论文作者
论文摘要
我们研究了SP（N+1）的四参数家族的RICCI流动在球体上的指标。我们确定它们的前瞻性行为，并对古代解决方案进行分类。在此过程中，我们在领域展示了一个新的单参数古代解决方案家族。这些（非等法）古代溶液都有一个较大的等轴测组，即SP（N+1）SP（1），SP（N+1）U（1）或U（2N+2）。在向后流下，两种古老的解决方案是非汇合的，并汇聚到了詹森的第二个爱因斯坦公制。一种解决方案参数众所周知的Berger指标。其余的是新的和崩溃的，在向后流的重新缩放下，齐勒在复杂的投影空间上的第二个同质爱因斯坦公制。
We study the Ricci flow of the four-parameter family of Sp(n+1)-invariant metrics on spheres. We determine their forward behaviour and also classify ancient solutions. In doing so, we exhibit a new one-parameter family of ancient solutions on spheres. These (non-isometric) ancient solutions all have a larger isometry group, namely Sp(n+1)Sp(1), Sp(n+1)U(1), or U(2n+2). Two ancient solutions are non-collapsed and converge, under the backwards flow, to Jensen's second Einstein metric. One solution parametrizes the well known Berger metrics. The rest are new and collapse, under a rescaling of the backwards flow, to Ziller's second homogeneous Einstein metric on complex projective space.
