The Periodic Orbit Conjecture for Steady Euler Flows

The periodic orbit conjecture states that, on closed manifolds, the set of lengths orbits a non-vanishing vector field all whose are admits an upper bound. This is known to be false in general due counterexample by Sullivan. However, it satisfied under geometric condition being geodesible. In this work, we use recent characterization Eulerisable flows (or more generally admitting strongly adapted one-form) prove that remains true for larger class fields.