Hi, All: Let X be a Reeb vector field, and let ω be a 1-form dual to X. Is ω necessarily a contact form? I know if we have a contact 1-form θ , and Zθ is the Reeb field associated with θ , then from the definition of Reeb field, we have θ (Zθ)=1, which mostly means that θ is nowhere zero, and we can rescale it to make it be 1 . But is the opposite the case, i.e., if θ (Rθ)=1 , does it follow that Rθ is the Reeb field associated to θ ? It seems like, since we're in a 1-dimensional situation, there isn't much room to maneuver and get different things. Thanks.