# Eigenvalue of a form

We are defining following form: $$\sum_{i,j}\partial_{z_i}\partial_{\bar{z_j}}rdz_i\otimes d\bar{z_j}$$
Where $r: M(\subset \mathbb C^2) \to \mathbb R$ is $C^2$ function.
1- Where this form acts[Domain]; I think $dz_i\otimes d\bar{z_i}$ should act on $\mathbb C\times \mathbb C$. But how does it act.. etc.
 Hi Junu, what is your background with tensor products? en.wikipedia.org/wiki/Tensor_product – tentaclenorm May 6 '12 at 4:51 @tentaclenorm, I know that $dz_i\otimes d\bar{z_i}$ should act on $\mathbb C\times \mathbb C$. But how does it act.. etc.. i think, i know a bit of tensor.. but i am confused.. – Junu May 6 '12 at 5:03