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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1911.13052 |
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| _version_ | 1866915087908864000 |
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| author | Podestà, Fabio Raffero, Alberto |
| author_facet | Podestà, Fabio Raffero, Alberto |
| contents | We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G$_2$-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is one-dimensional and the manifold is the Riemannian product of a flat factor and a non-compact homogeneous six-dimensional manifold endowed with an invariant strictly symplectic half-flat SU(3)-structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_13052 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Closed G$_2$-structures with a transitive reductive group of automorphisms Podestà, Fabio Raffero, Alberto Differential Geometry We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G$_2$-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is one-dimensional and the manifold is the Riemannian product of a flat factor and a non-compact homogeneous six-dimensional manifold endowed with an invariant strictly symplectic half-flat SU(3)-structure. |
| title | Closed G$_2$-structures with a transitive reductive group of automorphisms |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1911.13052 |