Surface Integrals of Differential 2-forms
Let
be a differential 2-form defined on the surface S, and let
be an orientation preserving parametrization of S with in D. Then, the surface integral of f on S is given by
where
is the surface element normal to S.
Let us note that the surface integral of this 2-form is the same as the surface integral of the vector field which has as components, and .
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