Jet Spaces as Nonrigid Carnot Groups

By B. Warhurst. Journal of Lie theory, 2005

54 citations recorded by the source corpus.

We dene 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-Backlund setting. Therefore, by prolonga- tion, they are nonrigid Carnot groups, meaning that the space of contact maps is innite dimensional. We also show that strata dimensions are not rigidity in- variants. This is demonstrated by constructing two distinct Carnot groups with strata dimensions (3; 2; 1) but with opposite rigidity. Mathematics Subject Classication: 53C24, 22E25

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

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Citations in the corpus

Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups (2009, background): “The general jet space Carnot groups Jk(Rm,Rn) (see [60]) also admit a presentation in which left translation is a Euclidean affine map.”