Isometric embeddings into Heisenberg groups

摘要: We study isometric embeddings of a Euclidean space or Heisenberg group into higher dimensional group, where both the source and target are equipped with an arbitrary left-invariant homogeneous distance that is not necessarily sub-Riemannian. show if all infinite geodesics in straight lines, then such embedding must be homomorphism. discuss necessary certain sufficient conditions for to have this `geodesic linearity property', we provide various examples.