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TakuyaMurata (talk | contribs) →Basic or tensorial forms on principal bundles: connection |
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Now, suppose there is a connection on ''P'' so that there is an [[exterior covariant differentiation]] ''D'' on (various) vector-valued forms on ''P''. Through the above correspondence, ''D'' also acts on ''E''-valued forms: define ∇ by
:<math>\nabla \overline{\phi} = \overline{D \phi}.</math>
In particular for zero-forms,
:<math>\nabla: \Gamma(M, E) \to \Gamma(M, T^*M \otimes E)</math>.
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