Smooth torus actions are described by a single vector field

  • Francisco Javier Turiel

    Universidad de Málaga, Spain
  • Antonio Viruel

    Universidad de Málaga, Spain
Smooth torus actions are described by a single vector field cover
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Abstract

Consider a smooth effective action of a torus Tn\mathbb T^n on a connected CC^{\infty}-manifold MM. Assume that MM is not a torus endowed with the natural action. Then we prove that there exists a complete vector field XX on MM such that the automorphism group of XX equals Tn×R\mathbb T^n \times \mathbb R, where the factor R\mathbb R comes from the flow of XX and Tn\mathbb T^n is regarded as a subgroup of Diff(M)(M). Thus one may reconstruct the whole action of Tn\mathbb T^n from a single vector field.

Cite this article

Francisco Javier Turiel, Antonio Viruel, Smooth torus actions are described by a single vector field. Rev. Mat. Iberoam. 34 (2018), no. 2, pp. 839–852

DOI 10.4171/RMI/1005