Conformal and CR mappings on Carnot groups
Differential Geometry
2019-11-04 v2 Metric Geometry
Abstract
We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and affine in each component.
Cite
@article{arxiv.1807.00994,
title = {Conformal and CR mappings on Carnot groups},
author = {Michael G. Cowling and Ji Li and Alessandro Ottazzi and Qingyan Wu},
journal= {arXiv preprint arXiv:1807.00994},
year = {2019}
}