Higher Elastica: Geodesics in the Jet Space
Dynamical Systems
2022-10-18 v1
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 . We show that its geodesic flow is integrable and that its geodesics generalize Euler's elastica, with the case corresponding to the elastica, as shown by Sachkov and Ardentov.
Cite
@article{arxiv.2003.08022,
title = {Higher Elastica: Geodesics in the Jet Space},
author = {Alejandro Bravo-Doddoli},
journal= {arXiv preprint arXiv:2003.08022},
year = {2022}
}