Abstract
AbstractCarnot groups are subRiemannian manifolds. As such, they admit geodesic flows, which are left-invariant Hamiltonian flows on their cotangent bundles. Some of these flows are integrable; some are not. The k-jets space of for real-valued functions on the real line forms a Carnot group of dimension $$k+2$$
k
+
2
. In this study, it is shown that its geodesic flow is integrable and that its geodesics generalize Euler’s elastica, with the case $$k=2$$
k
=
2
corresponding to the elastica.
Publisher
Springer Science and Business Media LLC
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