Re: Frobenius' Theorem

On Aug 22, 12:13 pm, Jing M Lim <jingobi...@xxxxxxxxx> wrote:
I have two problems that could probably be solved with Frobenius'
theorem.

1.) Show that any 2-form w on a 3-manifold is decomposable, i.e. there
are 1-forms a and b such that w = a ^ b.

2.) Let w be a closed 2-form on an n-manifold. For any point p where w
=/= 0, show that there is a coordinate neighborhood (x,U) around p
such that w = dx^1 ^ dx^2 .

For #2 it should say that w is a closed, decomposable 2-form.

.

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