Balogh, Zoltán M. Fässler, Katrin Sobrino, Hernando 2018-08-01 We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher dimensional Heisenberg group, where both the source and target space are equipped with an arbitrary left-invariant homogeneous distance that is not necessarily sub-Riemannian. We show that if all infinite geodesics in the target are straight lines, then such an embedding must be a homogeneous homomorphism. We discuss a necessary and certain sufficient conditions for the target space to have this ‘geodesic linearity property’, and we provide various examples. application/pdf https://folia.unifr.ch/global/documents/307074 https://folia.unifr.ch/documents/307074/files/fae_iei.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s10711-017-0282-5 info:eu-repo/semantics/openAccess License undefined Geometriae Dedicata. - 2018, vol. 195, no. 1, p. 163–192 info:eu-repo/classification/udc/51 Isometric embeddings into Heisenberg groups http://purl.org/coar/resource_type/c_6501