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
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Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2
  • Eero Hakavuori
  • Mathematics, Computer Science
  • SIAM J. Control. Optim.
  • 2020
It is proved that all infinite geodesics are lines exactly when the induced norm on the horizontal space is strictly convex, and it is shown that all isometric embeddings between such homogeneous groups are affine. Expand


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