Curvature Form - Definition

Definition

Let G be a Lie group with Lie algebra, and PB be a principal G-bundle. Let ω be an Ehresmann connection on P (which is a -valued one-form on P).

Then the curvature form is the -valued 2-form on P defined by

Here stands for exterior derivative, is defined by and D denotes the exterior covariant derivative. In other terms,

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