Reducible Holonomy in Closed Torsion Geometries

Leander Stecker

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arXiv · 2602.01458

Reducible Holonomy in Closed Torsion Geometries

Leander Stecker

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Abstract

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-K\"ahler 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.

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Leander Stecker. 2026-02-01. Reducible Holonomy in Closed Torsion Geometries. https://arxiv.org/abs/2602.01458

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