Iso-contact embeddings of manifolds in co-dimension 2

Abstract

The purpose of this article is to study co-dimension 2 iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold (M2n−1,ξM) iso-contact embeds in a contact manifold (N2n+1,ξN), provided M contact embeds in (N,ξN) with a trivial normal bundle and the contact structure induced on M via this embedding is homotopic as an almost-contact structure to ξM. We apply this result to first establish that a closed contact 3--manifold having no 2--torsion in its second integral cohomology iso-contact embeds in the standard contact 5--sphere if and only if the first Chern class of the contact structure is zero. Finally, we discuss iso-contact embeddings of closed simply connected contact 5--manifolds.