A metric characterization of Carnot groups

2013/04/28 by Enrico Le Donne, Donne, Enrico Le · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1304.7493

openalex publication_date 2013/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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