Strict contactomorphisms are scarce

Abstract

The notion of non-projectible contact forms on a given compact manifold $M$ is introduced by the first-named author in [Ohb], the set of which he also shows is a residual subset of the set of (coorientable) contact forms, both in the case with a fixed contact structure and in the case without it. In this paper, we prove that for any non-projectible contact form $\hat{I}»$ the set, denoted by ${\text{Cont}}^{\text{st}}(M,\hat{I}»)$, consisting of strict contactomorphisms of $\hat{I}»$ is a a countable disjoint union of real lines $\mathbb{R}$, one for each connected component.

33 pages, comments welcome!, v2) The case with fixed contact structure added in the main theorem