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arXiv · 1706.02077

Isometric Embeddings into Heisenberg Groups

Zoltán M. Balogh·Katrin Fässler·Hernando Sobrino
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Abstract

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.

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Zoltán M. Balogh, Katrin Fässler, Hernando Sobrino. 2017-06-07. Isometric Embeddings into Heisenberg Groups. https://doi.org/10.1007/s10711-017-0282-5

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