Details

Autor(en) / Beteiligte

• Turiel, Francisco Javier
• Viruel, Antonio

Titel

Smooth torus actions are described by a single vector field

Ist Teil von

• Revista matemática iberoamericana, 2018-01, Vol.34 (2), p.839-852

Ort / Verlag

Zuerich, Switzerland: European Mathematical Society Publishing House

Erscheinungsjahr

2018

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Consider a smooth effective action of a torus $\mathbb T^n$ on a connected $C^{\infty}$-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 $\mathbb T^n \times \mathbb R$, where the factor $\mathbb R$ comes from the flow of $X$ and $\mathbb T^n$ is regarded as a subgroup of Diff$(M)$. Thus one may reconstruct the whole action of $\mathbb T^n$ from a single vector field.