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Peer-reviewedCC BY-SA 4.0Symmetry, Integrability and Geometry: Methods and Applications

Reducible Holonomy in Closed Torsion Geometries

  • Leander Stecker1
  1. 1Universität Leipzig, Germany
Open at sourceDOICite

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.

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Cite

BibTeXRIS
BibTeX
@article{stecker2026reducible,
  title = {{Reducible Holonomy in Closed Torsion Geometries}},
  author = {Leander Stecker},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications},
  year = {2026},
  month = oct,
  doi = {10.3842/sigma.2026.104},
  url = {https://sigma-journal.com/2026/104/},
  note = {CC BY-SA 4.0},
}
RIS
TY  - JOUR
TI  - Reducible Holonomy in Closed Torsion Geometries
AU  - Leander Stecker
PY  - 2026
DA  - 2026/10/29
JO  - Symmetry, Integrability and Geometry: Methods and Applications
DO  - 10.3842/sigma.2026.104
UR  - https://sigma-journal.com/2026/104/
AB  - 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.
SN  - 1815-0659
ER  -