A remark on the Reeb flow for spheres

Abstract

>We prove the non-triviality of the Reeb flow for the standard contact spheres $\mathbb{S}^{2n+1}, n \neq 3$, inside the fundamental group of their contactomorphism group. The argument uses the existence of homotopically non-trivial $2$-spheres in the space of contact structures of a $3$-Sasakian manifold.