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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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


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
  • MR Author ID: 867590
  • Email:
  • 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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 845-849
  • MSC (2010): Primary 53C17, 53C60, 22E25, 58D19
  • DOI:
  • MathSciNet review: 3283670