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First of all I would like to apologize, as my knowledge of differential geometry is not as good as it should be (I only took an introductory course for physicists).

Anyhow, here is a question for you. Any help is greatly appreciated!

-I have a four dimensional manifold, whose properties are rather banal (for instance, all closed differential forms are also exact).

-On this manifold, I am given a nowhere-vanishing 1-form (I call it "dt").

-I would like to know if this nowhere-vanishing exact 1-form "dt" determines a foliation (the folia are t=const surfaces).

An attempt to an answer: dt is an exact 1-form, and t is a function (which maps points in the manifold to real numbers). Now, if dt is nowhere zero, t is a monotonic function. The surfaces of t=const are thus folia which are monotonically labeled.

Related topics: Frobenius theorem, space+time foliation

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# Nonzero exact 1-form implies foliation?

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