Curvature Form
The curvature form of a principal G-connection ω is the -valued 2-form Ω defined by
It is G-equivariant and horizontal, hence corresponds to a 2-form on M with values in . The identification of the curvature with this quantity is sometimes called the second structure equation.
Read more about this topic: Connection (principal Bundle)
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“Thought is the seed of action; but action is as much its second form as thought is its first.”
—Ralph Waldo Emerson (1803–1882)