Isometric embeddings into Heisenberg groups

Balogh, Zoltán M.; Fässler, Katrin; Sobrino, Hernando

doi:10.1007/s10711-017-0282-5

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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