Reeb orbit and open books

Question

Weinstein conjecture is about existence of a closed orbit of the Reeb vector field on every contact manifold. On the other hand, we know every contact 3-manifold admits a compatible open book, which implies the binding is tangent to the Reeb vector field, doesn't this imply the Weinstein conjecture? since the binding is a closed orbit of the Reeb flow?

Answer 1

Weinstein's Conjecture is that every contact form on every closed 3-manifold has a closed Reeb orbit. This is stronger than requiring that every contact manifold admit a defining 1-form with a closed Reeb orbit.