Smooth torus actions are described by a single vector field

Autor:	Francisco Javier Turiel, Antonio Viruel
Rok vydání:	2018
Předmět:	Pure mathematics Automorphism group Flow (mathematics) General Mathematics Torus Vector field Mathematics::Geometric Topology Mathematics::Symplectic Geometry Effective action Action (physics) Mathematics
Zdroj:	Revista Matemática Iberoamericana. 34:839-852
ISSN:	0213-2230
DOI:	10.4171/rmi/1005
Popis:	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.
Databáze:	OpenAIRE
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