An Application of Convex Integration to Contact Geometry

We prove that every closed, orientable -manifold admits a parallelization by the Reeb vector fields of a triple of contact forms with equal volume form. Our proof is based on Gromov's convex integration technique and the -principle. Similar methods can be used to show that admits a parallelization by contact forms with everywhere linearly independent Reeb vector fields. We also prove a generalization of this latter result to higher dimensions. If is a closed -manifold with contact form whose contact distribution admits everywhere linearly independent sections, then admits linearly independent contact forms with linearly independent Reeb vector fields.