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
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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
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 322903
- DOI 10.1007/s10711-017-0282-5
- Persistent URL
- https://folia.unifr.ch/unifr/documents/307074
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