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 $(M^{2n-1}, \xi_M)$ iso‑contact embeds in a contact manifold $(N^{2n+1}, \xi_N)$, 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.

Full Text (PDF format)

Received 10 June 2020

Accepted 13 August 2021

Published 23 December 2022