What is the One Form Needed for Div and Curl in 3-Space?

[SeReNiTy]

Can someone please point me in the direction of the one form required for my starting point producing the div and curl in 3space?

I know grad is simply the d operator
and div is *d*
curl is *d

i want to know what the one form i need to operate on to produce the classical div and curl formulas.

 

[Hurkyl]

Classically, div and curl act on vector fields, right? So how do you turn a vector field into a one-form?

 

[Hurkyl]

Right; you contract it with the metric.