# Homework Help: Raising and lowering differential forms

1. Jan 28, 2009

### toqp

1. The problem statement, all variables and given/known data
Calculate the contravariant components of the differential 1-form
$$\omega|_x = x^3 dx^1 - (x^2)^2 dx^3$$
that is raise it into $$\omega ^\#|_x$$

$$\eta ^{\mu\nu}(x)=diag(1,-1,-1,-1)$$

3. The attempt at a solution
I'm at lost here. I don't really understand how these differential forms work.

Can I just transfer the 1-form into an ordinary covector
$$\omega | _\nu=(0,x^3,0,-(x^2)^2)$$

and then raise it using
$$\eta ^{\mu\nu}\omega _\nu$$?