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

• Autorzy: Enrico Le Donne
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Carnot groups; sub-Riemannian geometry; sub-Finsler geometry; homogeneous spaces; homogeneous groups; nilpotent groups; metric groups

Kategorie tematyczne

• 22F30: Homogeneous spaces
• 43A80: Analysis on other specific Lie groups
• 22E25: Nilpotent and solvable Lie groups
• 53C17: Sub-Riemannian geometry
• 14M17: Homogeneous spaces and generalizations

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 116-137

Daty

wydano

2017-12-20

otrzymano

2016-11-18

poprawiono

2017-09-07

zaakceptowano

2017-11-08

online

2017-12-29

Twórcy

autor

Enrico Le Donne

• ,

Identyfikatory

DOI

10.1515/agms-2017-0007