A metric characterization of Carnot groups

Le Donne, Enrico

doi:10.1090/S0002-9939-2014-12244-1

A metric characterization of Carnot groups
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Proc. Amer. Math. Soc. 143 (2015), 845-849 Request permission

Abstract:

We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically homogeneous.

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