Hofer metric from the contact point of view

Abstract

Given a manifold $M$ endowed with a contact 1-form $\alpha$, a bi-invariant pseudo-metric $\varrho_\alpha$ is introduced on $Cont(M,\alpha)$, the compactly supported identity component of the group of all strict contactomorphisms of $(M,\alpha)$. For $M$ open $\varrho_\alpha$ is a metric.