Curvature form

In differential geometry, the curvature form describes curvature of a connection on a principal bundle. It can be considered as an alternative to or generalization of the curvature tensor in Riemannian geometry.

Let G be a Lie group with Lie algebra ${\displaystyle {\mathfrak {g}}}$, and P → B be a principal G-bundle. Let ω be an Ehresmann connection on P (which is a ${\displaystyle {\mathfrak {g}}}$-valued one-form on P).

Then the curvature form is the ${\displaystyle {\mathfrak {g}}}$-valued 2-form on P defined by

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