论文标题
较高的Elastica：喷气空间中的测量学
Higher Elastica: Geodesics in the Jet Space
论文作者
论文摘要
Carnot群是次级歧管。因此，他们承认了大地的流量，它们是剩下的不变的哈密顿式流动的束束。这些流中的一些是可以集成的。有些不是。实现实际线路上实现功能的K-Jets空间形成了一个尺寸$ K+2 $的Carnot组。我们表明其测量流是可集成的，并且其大地测量学概括了Euler的Elastica，而Case $ K = 2 $对应于弹性弹性，如Sachkov和Ardentov所示。
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.
