On the automorphism group of a closed G$_2$-structure
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866913633085161472 |
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| author | Podestà, Fabio Raffero, Alberto |
| author_facet | Podestà, Fabio Raffero, Alberto |
| contents | We study the automorphism group of a compact 7-manifold $M$ endowed with a closed non-parallel G$_2$-structure, showing that its identity component is abelian with dimension bounded by min$\{6,b_2(M)\}$. This implies the non-existence of compact homogeneous manifolds endowed with an invariant closed non-parallel G$_2$-structure. We also discuss some relevant examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_06674 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the automorphism group of a closed G$_2$-structure Podestà, Fabio Raffero, Alberto Differential Geometry We study the automorphism group of a compact 7-manifold $M$ endowed with a closed non-parallel G$_2$-structure, showing that its identity component is abelian with dimension bounded by min$\{6,b_2(M)\}$. This implies the non-existence of compact homogeneous manifolds endowed with an invariant closed non-parallel G$_2$-structure. We also discuss some relevant examples. |
| title | On the automorphism group of a closed G$_2$-structure |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1801.06674 |