Isometric Embeddings into Heisenberg Groups
Metric Geometry
2017-11-27 v1
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.
Cite
@article{arxiv.1706.02077,
title = {Isometric Embeddings into Heisenberg Groups},
author = {Zoltán M. Balogh and Katrin Fässler and Hernando Sobrino},
journal= {arXiv preprint arXiv:1706.02077},
year = {2017}
}
Comments
29 pages