Francisco Javier Turiel Sandín, Antonio Angel Viruel Arbaizar
Consider a smooth effective action of a torus Tn on a connected C∞-manifold M. Assume that M is not a torus endowed with the natural action. Then we prove that there exists a complete vector field X on M such that the automorphism group of X equals Tn×R, where the factor R comes from the flow of X and Tn is regarded as a subgroup of Diff(M). Thus one may reconstruct the whole action of Tn from a single vector field.
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