Reynolds transport theorem for smooth deformations of currents on manifolds. (July 2015) - Falach, Lior; Segev, Reuven
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 manifoldS, 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 inS . The essence of the resulting computations is that the derivative operator is represented by the dual of the Lie derivative operation on smooth forms.