Balogh, Zoltan; Fässler, Katrin; Sobrino, Hernando (2018). Isometric embeddings into Heisenberg groups. Geometriae dedicata, 195(1), pp. 163-192. Springer 10.1007/s10711-017-0282-5
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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.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Balogh, Zoltan, Fässler, Katrin, Sobrino, Hernando |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1572-9168 |
Publisher: |
Springer |
Language: |
English |
Submitter: |
Olivier Bernard Mila |
Date Deposited: |
17 Apr 2018 08:37 |
Last Modified: |
05 Dec 2022 15:09 |
Publisher DOI: |
10.1007/s10711-017-0282-5 |
BORIS DOI: |
10.7892/boris.109140 |
URI: |
https://boris.unibe.ch/id/eprint/109140 |
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