Smooth actions of connected compact Lie groups with a free point are determined by two vector fields
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866914757638881280 |
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| author | Turiel, F. J. Viruel, A. |
| author_facet | Turiel, F. J. Viruel, A. |
| contents | Consider a smooth action $\mathbf G\times M \rightarrow M$ of a compact connected Lie group $\mathbf G$ on a connected manifold $M$. Assume the existence of a point of $M$ whose isotropy group has a single element (free point). Then we prove that there exist two complete vector field $X,X_1$ such that their group of automorphisms equals $\mathbf G$ regarded as a group of diffeomorphisms of $M$ (the existence of a free point implies that the action of $\mathbf G$ is effective). Moreover, some examples of effective actions with no free point where this result fails are exhibited. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_11299 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Smooth actions of connected compact Lie groups with a free point are determined by two vector fields Turiel, F. J. Viruel, A. Differential Geometry 57R25, 57S15 Consider a smooth action $\mathbf G\times M \rightarrow M$ of a compact connected Lie group $\mathbf G$ on a connected manifold $M$. Assume the existence of a point of $M$ whose isotropy group has a single element (free point). Then we prove that there exist two complete vector field $X,X_1$ such that their group of automorphisms equals $\mathbf G$ regarded as a group of diffeomorphisms of $M$ (the existence of a free point implies that the action of $\mathbf G$ is effective). Moreover, some examples of effective actions with no free point where this result fails are exhibited. |
| title | Smooth actions of connected compact Lie groups with a free point are determined by two vector fields |
| topic | Differential Geometry 57R25, 57S15 |
| url | https://arxiv.org/abs/2112.11299 |