The Reynolds transport theorem for the rate of change of an integral over an evolving domain is generalized. For a manifold B, a differentiable motion m of B in the manifold , an r-current T in B, and the sequence of images m(t)♯T of the current under the motion, we consider the rate of change of the action of the images on a smooth r-form in . The essence of the resulting computations is that the derivative operator is represented by the dual of the Lie derivative operation on smooth forms.
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