Mathematische Zeitschrift

, Volume 259, Issue 3, pp 617–629

A sufficient condition for nonrigidity of Carnot groups


DOI: 10.1007/s00209-007-0240-2

Cite this article as:
Ottazzi, A. Math. Z. (2008) 259: 617. doi:10.1007/s00209-007-0240-2


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)


Copyright information

© Springer-Verlag 2007

Authors and Affiliations

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