An exact form of positive integer degree 
on a smooth
manifold 
is a smooth differential k-form 
that can be written as
 |
where 
is the exterior
derivative and 
is a smooth differential (k-1)-form
on 
(Sadun 2016, p. 33).
For a one-form 
on a region 
,
exactness means that 
for a function 
of class 
, i.e., once continuously
differentiable, on 
. Every exact form is a closed
form, since 
(Sadun 2016, pp. 5-6).
