In an n dimensional space if you have a
the Hodge star operation maps this form
onto an n-p dimensional form.
If this seems familiar then it is, in Stokes' Theorem
you take the form over a certain space (the form being the
integral element, the space being the surface of the
object under consideration) and you map it to
(i.e. identify it with) a form of associated with the volume.
(bad explaination, sorry, anyone else?)