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RESEARCH PRODUCT

A metric characterization of Carnot groups

Enrico Le Donne

subject

Pure mathematicsGeodesicGeneral MathematicsApplied MathematicsMathematical analysisMetric Geometry (math.MG)Characterization (mathematics)symbols.namesakeMathematics - Metric GeometryHomogeneousCarnot groupsMetric (mathematics)symbolsFOS: MathematicsMathematics (all)Mathematics::Metric GeometryMathematics::Differential GeometrySubRiemannian geometryCarnot cycleCarnot groups; SubRiemannian geometry; Mathematics (all); Applied MathematicsAxiomMathematics

description

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.

yearjournalcountryeditionlanguage
2013-04-28
http://arxiv.org/abs/1304.7493