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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 Z_{θ}is the Reeb field associated with θ

, then from the definition of Reeb field, we have θ (Z_{θ})=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 (R_{θ})=1 , does it follow that R_{θ}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.

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# Is the Dual of a Reeb field a Contact Form?

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