A metric characterization of Carnot groups
Enrico Le Donne
TL;DR
This paper provides an axiomatic framework for understanding Carnot groups through their metric properties, characterizing them as proper geodesic spaces with dilations and isometric homogeneity.
Contribution
It offers a new metric characterization of Carnot groups, linking their geometric structure to specific metric axioms and properties.
Findings
Carnot groups can be characterized as proper geodesic spaces with dilations
They are exactly the isometrically homogeneous spaces admitting dilations
The paper connects subRiemannian and subFinsler geometries to metric axioms
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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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology · Advanced Differential Geometry Research