De Rham derivative of a differential 1-form

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Definition

Definition by formula

Let M be a differential manifold. Let \omega be a differential 1-form, i.e. a section of the cotangent bundle T^*M. We define d\omega as the following alternating 2-form:

(d\omega)(X,Y) := X(\omega Y) - Y(\omega X) - \omega([X,Y])