Reducible Holonomy in Closed Torsion Geometries
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915953909956608 |
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| author | Stecker, Leander |
| author_facet | Stecker, Leander |
| contents | The purpose of this note is to show that a connection with closed skewsymmetric torsion and reducible holonomy admits a locally defined Riemannian submersion together with a projected geometry on the base. We reframe known submersion results for non-Kähler Bismut Hermite Einstein manifolds and sHKT structures in this context. For homogeneous SKT structures on semi-simple Lie groups we obtain the holonomy decomposition leading to holomorphic submersions over generalized flag manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reducible Holonomy in Closed Torsion Geometries Stecker, Leander Differential Geometry 53B05, 53C29, 53B35, 32M10 The purpose of this note is to show that a connection with closed skewsymmetric torsion and reducible holonomy admits a locally defined Riemannian submersion together with a projected geometry on the base. We reframe known submersion results for non-Kähler Bismut Hermite Einstein manifolds and sHKT structures in this context. For homogeneous SKT structures on semi-simple Lie groups we obtain the holonomy decomposition leading to holomorphic submersions over generalized flag manifolds. |
| title | Reducible Holonomy in Closed Torsion Geometries |
| topic | Differential Geometry 53B05, 53C29, 53B35, 32M10 |
| url | https://arxiv.org/abs/2602.01458 |