Exterior covariant derivative

In the mathematical field of differential geometry, the exterior covariant derivative is an extension of the notion of exterior derivative to the setting of a differentiable principal bundle or vector bundle with a connection. == Definition == Let G be a Lie group and P → M be a principal G-bundle on a smooth manifold M. Suppose there is a connection on P; this yields a natural direct sum decomposition T u P = H u ⊕ V u {\displaystyle T_{u}P=H_{u}\oplus V_{u}} of each tangent space into the horizontal and vertical subspaces.

Source: Wikipedia — Exterior covariant derivative (CC BY-SA 4.0)

Exterior covariant derivative

In the mathematical field of differential geometry, the exterior covariant derivative is an extension of the notion of exterior derivative to the setting of a differentiable principal bundle or vector bundle with a connection. == Definition == Let G be a Lie group and P → M be a principal G-bundle on a smooth manifold M. Suppose there is a connection on P; this yields a natural direct sum decomposition T u P = H u ⊕ V u {\displaystyle T_{u}P=H_{u}\oplus V_{u}} of each tangent space into the horizontal and vertical subspaces.

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Source: Wikipedia "Exterior covariant derivative" · CC BY-SA 4.0

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