A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
Copyright policy )A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
AbstractCarnot 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.
- University of Pisa Italy
- University of Jyväskylä Finland
QA299.6-433, homogeneous groups, homogeneous spaces, metric groups, ryhmäteoria, sub-finsler geometry, nilpotent groups, Carnot groups; homogeneous groups; homogeneous spaces; metric groups; nilpotent groups; sub-Finsler geometry; sub-Riemannian geometry; Analysis; Geometry and Topology; Applied Mathematics, sub-riemannian geometry, differentiaaligeometria, sub-Riemannian geometry, 43a80, 53c17, Carnot groups, sub-Finsler geometry, carnot groups, Matematiikka, 22e25, 22f30, Mathematics, 14m17, Analysis
QA299.6-433, homogeneous groups, homogeneous spaces, metric groups, ryhmäteoria, sub-finsler geometry, nilpotent groups, Carnot groups; homogeneous groups; homogeneous spaces; metric groups; nilpotent groups; sub-Finsler geometry; sub-Riemannian geometry; Analysis; Geometry and Topology; Applied Mathematics, sub-riemannian geometry, differentiaaligeometria, sub-Riemannian geometry, 43a80, 53c17, Carnot groups, sub-Finsler geometry, carnot groups, Matematiikka, 22e25, 22f30, Mathematics, 14m17, Analysis
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