Isometries of nilpotent metric groups

  title={Isometries of nilpotent metric groups},
  author={Ville Kivioja and Enrico Le Donne},
  journal={arXiv: Metric Geometry},
We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object metric Lie groups. Apart from Riemannian Lie groups, distinguished examples are sub-Riemannian Lie groups and, in particular, Carnot groups equipped with Carnot-Carath\'eodory distances. We study the regularity of isometries, i.e., distance-preserving homeomorphisms. Our first result is the analyticity of such maps… Expand
From homogeneous metric spaces to Lie groups
Isometric embeddings into Heisenberg groups
Metric Lie groups admitting dilations.