Isometric embeddings into Heisenberg groups

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)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan; Fässler, Katrin and 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:

03 Jul 2018 01:30

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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