# Curl over surface

1. Feb 9, 2014

### Jhenrique

If I can compute the divergence over an closed curve (or an area) and too over an closed surface (ie, an volume) so I can, actually, to compute the divergence over a n-manifold.
$$\nabla \cdot \vec{F} = \lim_{\Delta V → 0} \frac{1}{\Delta V} \oint_{S} \vec{F} \cdot \hat{n} dS$$$$\nabla \cdot \vec{F} = \lim_{\Delta A → 0} \frac{1}{\Delta A} \oint_{C} \vec{F} \cdot \hat{n} dr$$So, make sense speak about the curl of a 2-manifold? Do you undestand my ask? Exist a math formlation for the curl over a curve
$$(\nabla \times \vec{F}) \cdot \hat{n}= \lim_{\Delta S → 0} \frac{1}{\Delta S} \oint_{C} \vec{F} \cdot d\vec{r}$$but, exist for a surface?

Last edited: Feb 9, 2014