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A metric characterization of Carnot groups


Author: Enrico Le Donne
Journal: Proc. Amer. Math. Soc. 143 (2015), 845-849
MSC (2010): Primary 53C17, 53C60, 22E25, 58D19
DOI: https://doi.org/10.1090/S0002-9939-2014-12244-1
Published electronically: September 18, 2014
MathSciNet review: 3283670
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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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Additional Information

Enrico Le Donne
Affiliation: Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014, University of Jyväskylä, Finland
Email: enrico.e.ledonne@jyu.fi

DOI: https://doi.org/10.1090/S0002-9939-2014-12244-1
Keywords: Carnot groups, subRiemannian geometry
Received by editor(s): April 18, 2013
Received by editor(s) in revised form: April 28, 2013
Published electronically: September 18, 2014
Additional Notes: The author thanks IPAM and all of the people involved in the program, ‘Interactions Between Analysis and Geometry’, during which there was the opportunity to discuss these results
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.