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A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
Analysis and Geometry in Metric Spaces ( IF 1 ) Pub Date : 2018-01-04 , DOI: 10.1515/agms-2017-0007
Enrico Le Donne 1
Affiliation  

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 homogeneousmetric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups.

中文翻译:

卡诺群入门:齐次群、Carnot-Carathéodory 空间及其等距的规律性

卡诺群是结构丰富的特殊空间:它们是那些李群,其路径距离对于群的左平移是不变的,并且允许自同构,它们是关于距离的膨胀。介绍了卡诺群的基本理论并附上几点说明。我们把它们看作是分级群的特例和齐次度量空间。我们讨论了 Carnot-Carathéodory 空间和幂零度量李群的一般情况下的等距的正则性。
更新日期:2018-01-04
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