Submersion constructions for geometries with parallel skew torsion
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913512870117376 |
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| author | Moroianu, Andrei Schwahn, Paul |
| author_facet | Moroianu, Andrei Schwahn, Paul |
| contents | In the absence of a de Rham decomposition theorem for geometries with torsion, we develop and unify ways to view a geometry with parallel skew torsion as the total space of a locally defined, not necessarily unique Riemannian submersion with totally geodesic fibers. We complete and extend the Cleyton-Swann classification of irreducible such geometries and characterize the cases where the stabilizer of the torsion is larger than the holonomy. As a byproduct, we obtain structure results on Gray manifolds, nearly parallel G$_2$-manifolds and Sasaki manifolds with reducible holonomy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_14421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Submersion constructions for geometries with parallel skew torsion Moroianu, Andrei Schwahn, Paul Differential Geometry 53B05, 53C25 In the absence of a de Rham decomposition theorem for geometries with torsion, we develop and unify ways to view a geometry with parallel skew torsion as the total space of a locally defined, not necessarily unique Riemannian submersion with totally geodesic fibers. We complete and extend the Cleyton-Swann classification of irreducible such geometries and characterize the cases where the stabilizer of the torsion is larger than the holonomy. As a byproduct, we obtain structure results on Gray manifolds, nearly parallel G$_2$-manifolds and Sasaki manifolds with reducible holonomy. |
| title | Submersion constructions for geometries with parallel skew torsion |
| topic | Differential Geometry 53B05, 53C25 |
| url | https://arxiv.org/abs/2409.14421 |