Geometries with parallel, skew-symmetric and closed torsion
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910215705722880 |
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| author | Moroianu, Andrei Schwahn, Paul |
| author_facet | Moroianu, Andrei Schwahn, Paul |
| contents | We study Riemannian manifolds carrying a metric connection with parallel, skew-symmetric and closed torsion, which we call in short PSCT manifolds. We prove that PSCT manifolds always locally split into a product of well-understood factors, allowing a complete local classification. Further, we investigate various $G$-structures of PSCT type, with a focus on almost Hermitian structures and their possible Gray--Hervella classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13227 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometries with parallel, skew-symmetric and closed torsion Moroianu, Andrei Schwahn, Paul Differential Geometry 53B05, 53C10, 53C15, 53C25 We study Riemannian manifolds carrying a metric connection with parallel, skew-symmetric and closed torsion, which we call in short PSCT manifolds. We prove that PSCT manifolds always locally split into a product of well-understood factors, allowing a complete local classification. Further, we investigate various $G$-structures of PSCT type, with a focus on almost Hermitian structures and their possible Gray--Hervella classes. |
| title | Geometries with parallel, skew-symmetric and closed torsion |
| topic | Differential Geometry 53B05, 53C10, 53C15, 53C25 |
| url | https://arxiv.org/abs/2605.13227 |