# Manifolds with nonwhere vanishing closed one forms

I am trying to find examples of closed manifolds $$M$$ admitting a nowhere vanishing closed one form. I am wondering if there are any examples beyond $$N\times S^1$$.

If $$f: M \to S^1$$ is a submersion (and so a fiber bundle if $$M$$ is compact) then $$f^*d\theta$$ is a nowhere-vanishing closed 1-form. There are many more such manifolds and fibrations than just products, and the manifolds have the name mapping tori.
If $$(M,\omega)$$ is a manifold equipped with a nowhere vanishing closed 1-form, then in fact there is a fibration over the circle $$f: M \to S^1$$ so that $$f^*d\theta$$ is arbitrarily close to $$\omega$$. This is a theorem of Tischler, whose short proof can be read here.