SIGMA 22 (2026), 104, 16 pages      arXiv:2602.01458      https://doi.org/10.3842/SIGMA.2026.104

Reducible Holonomy in Closed Torsion Geometries

Leander Stecker
Universität Leipzig, Augustusplatz 10, 04109 Leipzig, Germany

Received May 01, 2026, in final form October 12, 2026; Published online October 29, 2026

Abstract
The purpose of this note is to show that a connection with closed skew-symmetric 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.

Key words: closed torsion connection; holonomy; Riemannian submersions; SKT manifolds; homogeneous SKT spaces.

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