Mathematische Zeitschrift

, Volume 259, Issue 3, pp 617–629 | Cite as

A sufficient condition for nonrigidity of Carnot groups



In this article we consider contact mappings on Carnot groups. Namely, we are interested in those mappings whose differential preserves the horizontal space, defined by the first stratum of the natural stratification of the Lie algebra of a Carnot group. We give a sufficient condition for a Carnot group G to admit an infinite dimensional space of contact mappings, that is, for G to be nonrigid. A generalization of Kirillov’s Lemma is also given. Moreover, we construct a new example of nonrigid Carnot group.

Mathematics Subject Classification (2000)

22E25 22E60 53D10 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BernBernSwitzerland
  2. 2.DIMAUniversità di GenovaGenova (1)Italy

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