Hi guys!(adsbygoogle = window.adsbygoogle || []).push({});

I am reading a paper which uses closed forms [tex] \omega [/tex] on a p-dimensional closed submanifold [tex] \Sigma[/tex] of a larger manifold [tex]M[/tex]. When we integrate [tex]\omega[/tex] we get a number

[tex] Q(\Sigma) =\int _{\Sigma}\omega [/tex] which, in principle, depends on the choice of [tex]\Sigma [/tex] but because [tex] \omega [/tex]is closed, [tex] Q(\Sigma)[/tex] is said to be unchanged by continuous deformations of [tex]\Sigma[/tex]. The converse is supposed to be true as well.

Now, I understand this as a generalization of Gauss' law in electrostatics (three dimensions) but I only remember that for this particular case, the demonstration I saw was purely geometrical. I know that this has to use the fact that [tex] \Sigma [/tex] does not have a boundary (closed submanifold). How exactly is this proved?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integration of closed forms

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**