In this paper, we consider the Yamabe flow on Lie groups with left invariant metrics in particular case on the higher dimensional classical Heisenberg nilpotent Lie groups and the higher dimensional quaternion Lie groups. We construct a explicit solution of the Yamabe flow on each group. Then we investigate the some properties on these Lie groups under the Yamabe flow. At the end of paper, we study the deformation of some feature of compact nilmanifolds \(\Gamma {\setminus } N\) under the Yamabe flow, where N is a simply connected two-step nilpotent Lie group with a left invariant metric, and \(\Gamma \) is a discrete cocompact subgroup of N, in particular Heisenberg and quaternion Lie groups.

中文翻译：

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Yamabe流在无能谎言群体上

在本文中，我们考虑具有左不变度量的Lie群上的Yamabe流，特别是在高维经典Heisenberg幂等Lie群和高维四元数Lie群上。我们为每个组构造Yamabe流的显式解决方案。然后，我们研究了Yamabe流下这些Lie群的一些性质。在论文的最后，我们研究了在Yamabe流下的紧紧的尼尔曼褶皱\（\ Gamma {\ setminus} N \）的某些特征的变形，其中N是具有左不变度量的简单连接的两步幂等李群，和\（\ Gamma \）是N的一个离散的紧紧子群，尤其是Heisenberg和四元数Lie群。