Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Elastica: Geodesics in the Jet Space   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.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg