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arXiv · 2003.08022

Higher Elastica: Geodesics in the Jet Space

Alejandro Bravo-Doddoli
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Abstract

Carnot 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 space of k-jets for real-valued functions on the real line forms a Carnot group of dimension $k+2$. We show that its geodesic flow is integrable and that its geodesics generalize Euler's elastica, with the case $k=2$ corresponding to the elastica, as shown by Sachkov and Ardentov.

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Alejandro Bravo-Doddoli. 2020-03-18. Higher Elastica: Geodesics in the Jet Space. https://doi.org/10.1007/s40879-022-00574-0

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