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Let M {\displaystyle M} be a differential manifold. Let ω {\displaystyle \omega } be a differential 1-form, i.e. a section of the cotangent bundle T ∗ M {\displaystyle T^{*}M} . We define d ω {\displaystyle d\omega } as the following alternating 2-form:
( d ω ) ( X , Y ) := X ( ω Y ) − Y ( ω X ) − ω ( [ X , Y ] ) {\displaystyle (d\omega )(X,Y):=X(\omega Y)-Y(\omega X)-\omega ([X,Y])}
![{\displaystyle (d\omega )(X,Y):=X(\omega Y)-Y(\omega X)-\omega ([X,Y])}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1dc69c73dce2d20576a5956f2e6178985b8afbb)