Journal article

Isometric embeddings into Heisenberg groups

  • Balogh, Zoltán M. Department of Mathematics and Statistics, University of Bern, Switzerland
  • Fässler, Katrin Department of Mathematics, University of Fribourg, Switzerland
  • Sobrino, Hernando Department of Mathematics and Statistics, University of Bern, Switzerland - Department of Mathematics, University of Fribourg, Switzerland
    01.08.2018
Published in:
  • Geometriae Dedicata. - 2018, vol. 195, no. 1, p. 163–192
English 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.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/307074
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