Originally Posted by ManuelF
That is a necessary condition, but I do not think is enough!
Are you sure?
Thank you.
|
It is necessary and sufficient in Euclidean space.
For instance, in magnetostatics a magnetic field always has a vector potential.
If the field is B = (u,v,w) consider the 2 form udy^dz -vdx^dz + wdx^dy
Since B has zero divergence, the 2 form is closed. By Poincare's Lemma it is therefore the exterior derivative of a 1 form adx + bdy + cdx. The curl of (a,b,c) equals B.
