A primer on Carnot groups: homogenous groups, CC spaces, and regularity of their isometries
Metric Geometry
2016-04-29 v1 Differential Geometry
Group Theory
Abstract
Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks. We consider them as special cases of graded groups and as homogeneous metric spaces. We discuss the regularity of isometries in the general case of Carnot-Caratheodory spaces and of nilpotent metric Lie groups.
Keywords
Cite
@article{arxiv.1604.08579,
title = {A primer on Carnot groups: homogenous groups, CC spaces, and regularity of their isometries},
author = {Enrico Le Donne},
journal= {arXiv preprint arXiv:1604.08579},
year = {2016}
}
Comments
25 pages, survey written for a summer school on metric spaces