Definition
Let P → M be a principal G-bundle on a smooth manifold M. If ϕ is a tensorial k-form on P, then its exterior covariant derivative is defined by
where h denotes the projection to the horizontal subspace, Hx defined by the connection, with kernel Vx (the vertical subspace) of the tangent bundle of the total space of the fiber bundle. Here Xi are any vector fields on P. Dϕ is a tensorial (k + 1)-form on P.
Read more about this topic: Exterior Covariant Derivative
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