Journal of Lie Theory
Vol. 15, No. 1, pp. 341–356 (2005)
Jet spaces as nonrigid Carnot groups
Ben WarhurstB. Warhurst
School of Mathematics
Sydney 2052 Australia
Abstract: We define a product on the jet spaces $J^k(\R^m,\R^n)$ which makes them Carnot groups. The Carnot group contact structure coincides with the classical contact structure in the Lie-Bäcklund setting. Therefore, by prolongation, they are nonrigid Carnot groups, meaning that the space of contact maps is infinite dimensional. We also show that strata dimensions are not rigidity invariants. This is demonstrated by constructing two distinct Carnot groups with strata dimensions $(3,2,1)$ but with opposite rigidity.
Classification (MSC2000): 53C24, 22E25
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Electronic fulltext finalized on: 26 Aug 2004. This page was last modified: 4 Jun 2010.