Iso-contact embeddings of manifolds in co-dimension 2

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, xi(M)) iso-contact embeds in a contact manifold (N2n+1, xi(N)), provided M contact embeds in (N, xi(N)) with trivial normal bundle and the contact structure induced on M via this embedding is overtwisted and homotopic as an almost-contact structure to xi(M). We apply this result to show 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.