Contact and isocontact embedding of $\pi$-manifolds

TL;DR

This paper establishes new contact embedding theorems for closed $$-manifolds, extending smooth embedding results to the contact geometric setting and providing conditions for contact and isocontact embeddings.

Contribution

It proves contact and isocontact embedding theorems for $$-manifolds, including bounds on embedding dimensions and conditions related to bounding $$-manifolds.

Findings

Contact embedding of certain $$-manifolds into Euclidean space with standard contact structure.

Isocontact embedding results for $$-manifolds and parallelizable manifolds.

Extension of smooth embedding theorems to the contact geometric context.

Abstract

We prove some contact analogs of smooth embedding theorems for closed $\pi$-manifolds. We show that a closed, $k$-connected, $\pi$-manifold of dimension (2n + 1) that bounds a $\pi$-manifold, contact embeds in the $(4n-2k+3)$-dimensional Euclidean space with the standard contact structure. We also prove some isocontact embedding results for $\pi$-manifolds and parallelizable manifolds.