A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

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 togethe...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autor principal:	Le Donne Enrico
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2018
Materias:	carnot groups sub-riemannian geometry sub-finsler geometry homogeneous spaces homogeneous groups nilpotent groups metric groups 53c17 43a80 22e25 22f30 14m17 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/9cdfe596c6444463aa6275b34dbd783b
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:9cdfe596c6444463aa6275b34dbd783b
record_format	dspace
spelling	oai:doaj.org-article:9cdfe596c6444463aa6275b34dbd783b2021-12-05T14:10:38ZA Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries2299-327410.1515/agms-2017-0007https://doaj.org/article/9cdfe596c6444463aa6275b34dbd783b2018-01-01T00:00:00Zhttps://doi.org/10.1515/agms-2017-0007https://doaj.org/toc/2299-3274Carnot 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.Le Donne EnricoDe Gruyterarticlecarnot groupssub-riemannian geometrysub-finsler geometryhomogeneous spaceshomogeneous groupsnilpotent groupsmetric groups53c1743a8022e2522f3014m17AnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 5, Iss 1, Pp 116-137 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	carnot groups sub-riemannian geometry sub-finsler geometry homogeneous spaces homogeneous groups nilpotent groups metric groups 53c17 43a80 22e25 22f30 14m17 Analysis QA299.6-433
spellingShingle	carnot groups sub-riemannian geometry sub-finsler geometry homogeneous spaces homogeneous groups nilpotent groups metric groups 53c17 43a80 22e25 22f30 14m17 Analysis QA299.6-433 Le Donne Enrico A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
description	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.
format	article
author	Le Donne Enrico
author_facet	Le Donne Enrico
author_sort	Le Donne Enrico
title	A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
title_short	A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
title_full	A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
title_fullStr	A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
title_full_unstemmed	A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
title_sort	primer on carnot groups: homogenous groups, carnot-carathéodory spaces, and regularity of their isometries
publisher	De Gruyter
publishDate	2018
url	https://doaj.org/article/9cdfe596c6444463aa6275b34dbd783b
work_keys_str_mv	AT ledonneenrico aprimeroncarnotgroupshomogenousgroupscarnotcaratheodoryspacesandregularityoftheirisometries AT ledonneenrico primeroncarnotgroupshomogenousgroupscarnotcaratheodoryspacesandregularityoftheirisometries
_version_	1718371854458028032

A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

Ejemplares similares