论文标题
Ricci流的对称性
Symmetries of Ricci Flows
论文作者
论文摘要
在目前的工作中，我们发现Ricci流的Lie Point对称性在$ n $ dimensional的歧管上。我们介绍了一种方法，以重新将这些对称性重新授予以获得特定指标的谎言点对称性。我们应用这种方法来检索爱因斯坦方程的谎言点对称性 - 被视为“静态” ricci流，以及某些特定类型的感兴趣指标，例如在折射产物上。最后，我们使用发现的对称性来为所考虑的特定指标家族获得RICCI流量的不变解决方案。
In the present work we find the Lie point symmetries of the Ricci flow on an $n$-dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this method to retrieve the Lie point symmetries of the Einstein equations -- seen as a "static" Ricci flow -- , and of some particular types of metrics of interest, such as, on warped products of manifolds. Finally, we use the symmetries found to obtain invariant solutions of the Ricci flow for the particular families of metrics considered.
