Metric Lie groups admitting dilations

@article{Donne2019MetricLG,
  title={Metric Lie groups admitting dilations},
  author={Enrico Le Donne and S. Golo},
  journal={arXiv: Metric Geometry},
  year={2019}
}
We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $ d(\delta_\lambda x,\delta_\lambda y) = \lambda d(x,y)$, for all $x,y\in G$ and all $\lambda>0$. First, we show that all such distances are admissible, that is, they induce the manifold topology. Second, we characterize multiplicative one-parameter groups of Lie… Expand
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