The curvature form of a connection with matrix-valued connection 1-form 
is the 2-form 
.
It measures the failure of covariant derivatives
to commute and transforms covariantly under a change of local frame.
Curvature Form
See also
Connection, Curvature, Differential k-Form, Exterior DerivativeExplore with Wolfram|Alpha
References
Kobayashi, S. and Nomizu, K. Foundations of Differential Geometry, Vol. 1. New York: Wiley, 1963.Cite this as:
Weisstein, Eric W. "Curvature Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CurvatureForm.html