A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
Le Donne, E. (2017). A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries. Analysis and Geometry in Metric Spaces, 5 (1), 116-137. doi:10.1515/agms-2017-0007
Julkaistu sarjassaAnalysis and Geometry in Metric Spaces
© 2017 Enrico Le Donne, published by De Gruyter Open. This is an open access article distributed under the terms of the Creative Commons License.
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-Carathéodory spaces and of nilpotent metric Lie groups.