论文标题
$ \ mathbb {r}^{2n} \ times s^1 $ of contactomormormormisms of Contactomormormisms组的测量学
Geodesics of norms on the contactomorphisms group of $\mathbb{R}^{2n} \times S^1$
论文作者
论文摘要
我们证明，$ \ mathbb {r}^{2n} \ times s^1 $具有其标准接触结构的某些接触型途径是针对紧凑型触点触点的身份组成部分定义的不同规范的地理学及其通用触点及其通用封面。我们通过提供产生的哈密顿量功能的条件来表征这些大地测量学。对于每一个规范，我们都表明，可以用相应的哈密顿函数的绝对值的最大值表示，这是这种大地测量的时间。特别是我们恢复了这些规范是无限的事实
We prove that some paths of contactomorphisms of $\mathbb{R}^{2n} \times S^1$ endowed with its standard contact structure are geodesics for different norms defined on the identity component of the group of compactly supported contactomorphisms and its universal cover. We characterize these geodesics by giving conditions on the Hamiltonian functions that generate them. For every norm considered we show that the norm of a contactomorphism that is the time-one of such a geodesic can be expressed in terms of the maximum of the absolute value of the corresponding Hamiltonian function. In particular we recover the fact that these norms are unbounded
