The bundle curvature of a vector bundle connection 
on a vector
bundle 
is the 2-form 
with values in the vector
bundle of endomorphisms of 
. Equivalently, for vector fields 
and 
and a bundle section 
,
![Omega(X,Y)s=del _Xdel _Ys-del _Ydel _Xs-del _([X,Y])s.](/images/equations/BundleCurvature/NumberedEquation1.svg) |
In a local trivialization in which 
for a matrix 
of one-forms, the curvature
is
 |
A vector bundle connection is called flat when its bundle curvature vanishes.
