A sufficient condition for nonrigidity of Carnot groups |
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Authors: | Alessandro Ottazzi |
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Institution: | 1.Mathematisches Institut,Universit?t Bern,Bern,Switzerland;2.DIMA,Università di Genova,Genova (1),Italy |
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Abstract: | 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.
This research was partly supported by the Swiss National Science Foundation. The author would like to thank H. M. Reimann
for the helpful advices and the constant support. |
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Keywords: | 22E25 22E60 53D10 |
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